<?php
    /** PHPExcel root directory */
    if (!defined('PHPEXCEL_ROOT')) {
        /**
         * @ignore
         */
        define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../');
        require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
    }
    if (!defined('CALCULATION_REGEXP_CELLREF')) {
        //    Test for support of \P (multibyte options) in PCRE
        if (defined('PREG_BAD_UTF8_ERROR')) {
            //    Cell reference (cell or range of cells, with or without a sheet reference)
            define('CALCULATION_REGEXP_CELLREF', '((([^\s,!&%^\/\*\+<>=-]*)|(\'[^\']*\')|(\"[^\"]*\"))!)?\$?([a-z]{1,3})\$?(\d{1,7})');
            //    Named Range of cells
            define('CALCULATION_REGEXP_NAMEDRANGE', '((([^\s,!&%^\/\*\+<>=-]*)|(\'[^\']*\')|(\"[^\"]*\"))!)?([_A-Z][_A-Z0-9\.]*)');
        } else {
            //    Cell reference (cell or range of cells, with or without a sheet reference)
            define('CALCULATION_REGEXP_CELLREF', '(((\w*)|(\'[^\']*\')|(\"[^\"]*\"))!)?\$?([a-z]{1,3})\$?(\d+)');
            //    Named Range of cells
            define('CALCULATION_REGEXP_NAMEDRANGE', '(((\w*)|(\'.*\')|(\".*\"))!)?([_A-Z][_A-Z0-9\.]*)');
        }
    }

    /**
     * PHPExcel_Calculation (Multiton)
     * Copyright (c) 2006 - 2015 PHPExcel
     * This library is free software; you can redistribute it and/or
     * modify it under the terms of the GNU Lesser General Public
     * License as published by the Free Software Foundation; either
     * version 2.1 of the License, or (at your option) any later version.
     * This library is distributed in the hope that it will be useful,
     * but WITHOUT ANY WARRANTY; without even the implied warranty of
     * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
     * Lesser General Public License for more details.
     * You should have received a copy of the GNU Lesser General Public
     * License along with this library; if not, write to the Free Software
     * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
     * @category   PHPExcel
     * @package    PHPExcel_Calculation
     * @copyright  Copyright (c) 2006 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
     * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
     * @version    ##VERSION##, ##DATE##
     */
    class PHPExcel_Calculation {
        /** Constants                */
        /** Regular Expressions        */
        //    Numeric operand
        const CALCULATION_REGEXP_NUMBER = '[-+]?\d*\.?\d+(e[-+]?\d+)?';
        //    String operand
        const CALCULATION_REGEXP_STRING = '"(?:[^"]|"")*"';
        //    Opening bracket
        const CALCULATION_REGEXP_OPENBRACE = '\(';
        //    Function (allow for the old @ symbol that could be used to prefix a function, but we'll ignore it)
        const CALCULATION_REGEXP_FUNCTION = '@?([A-Z][A-Z0-9\.]*)[\s]*\(';
        //    Cell reference (cell or range of cells, with or without a sheet reference)
        const CALCULATION_REGEXP_CELLREF = CALCULATION_REGEXP_CELLREF;
        //    Named Range of cells
        const CALCULATION_REGEXP_NAMEDRANGE = CALCULATION_REGEXP_NAMEDRANGE;
        //    Error
        const CALCULATION_REGEXP_ERROR = '\#[A-Z][A-Z0_\/]*[!\?]?';
        /** constants */
        const RETURN_ARRAY_AS_ERROR = 'error';
        const RETURN_ARRAY_AS_VALUE = 'value';
        const RETURN_ARRAY_AS_ARRAY = 'array';
        /**
         * Locale-specific translations for Excel constants (True, False and Null)
         * @var string[]
         */
        public static  $localeBoolean     = [
            'TRUE'  => 'TRUE',
            'FALSE' => 'FALSE',
            'NULL'  => 'NULL'
        ];
        private static $returnArrayAsType = self::RETURN_ARRAY_AS_VALUE;
        /**
         * Instance of this class
         * @access    private
         * @var PHPExcel_Calculation
         */
        private static $instance;
        /**
         * List of instances of the calculation engine that we've instantiated for individual workbooks
         * @access    private
         * @var PHPExcel_Calculation[]
         */
        private static $workbookSets;
        /**
         * List of operators that can be used within formulae
         * The true/false value indicates whether it is a binary operator or a unary operator
         * @access    private
         * @var array
         */
        private static $operators = [
            '+'  => true,
            '-'  => true,
            '*'  => true,
            '/'  => true,
            '^'  => true,
            '&'  => true,
            '%'  => false,
            '~'  => false,
            '>'  => true,
            '<'  => true,
            '='  => true,
            '>=' => true,
            '<=' => true,
            '<>' => true,
            '|'  => true,
            ':'  => true
        ];
        /**
         * List of binary operators (those that expect two operands)
         * @access    private
         * @var array
         */
        private static $binaryOperators = [
            '+'  => true,
            '-'  => true,
            '*'  => true,
            '/'  => true,
            '^'  => true,
            '&'  => true,
            '>'  => true,
            '<'  => true,
            '='  => true,
            '>=' => true,
            '<=' => true,
            '<>' => true,
            '|'  => true,
            ':'  => true
        ];
        /**
         * The current locale setting
         * @var string
         */
        private static $localeLanguage = 'en_us';
        /**
         * List of available locale settings
         * Note that this is read for the locale subdirectory only when requested
         * @var string[]
         */
        private static $validLocaleLanguages = [
            'en'
            //    English        (default language)
        ];
        /**
         * Locale-specific argument separator for function arguments
         * @var string
         */
        private static $localeArgumentSeparator = ',';
        private static $localeFunctions         = [];
        /**
         * Excel constant string translations to their PHP equivalents
         * Constant conversion from text name/value to actual (datatyped) value
         * @var string[]
         */
        private static $excelConstants            = [
            'TRUE'  => true,
            'FALSE' => false,
            'NULL'  => null
        ];
        private static $PHPExcelFunctions         = [
            'ABS'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'abs',
                'argumentCount' => '1'
            ],
            'ACCRINT'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::ACCRINT',
                'argumentCount' => '4-7'
            ],
            'ACCRINTM'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::ACCRINTM',
                'argumentCount' => '3-5'
            ],
            'ACOS'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'acos',
                'argumentCount' => '1'
            ],
            'ACOSH'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'acosh',
                'argumentCount' => '1'
            ],
            'ADDRESS'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::CELL_ADDRESS',
                'argumentCount' => '2-5'
            ],
            'AMORDEGRC'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::AMORDEGRC',
                'argumentCount' => '6,7'
            ],
            'AMORLINC'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::AMORLINC',
                'argumentCount' => '6,7'
            ],
            'AND'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                'functionCall'  => 'PHPExcel_Calculation_Logical::LOGICAL_AND',
                'argumentCount' => '1+'
            ],
            'AREAS'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1'
            ],
            'ASC'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1'
            ],
            'ASIN'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'asin',
                'argumentCount' => '1'
            ],
            'ASINH'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'asinh',
                'argumentCount' => '1'
            ],
            'ATAN'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'atan',
                'argumentCount' => '1'
            ],
            'ATAN2'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::ATAN2',
                'argumentCount' => '2'
            ],
            'ATANH'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'atanh',
                'argumentCount' => '1'
            ],
            'AVEDEV'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::AVEDEV',
                'argumentCount' => '1+'
            ],
            'AVERAGE'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::AVERAGE',
                'argumentCount' => '1+'
            ],
            'AVERAGEA'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::AVERAGEA',
                'argumentCount' => '1+'
            ],
            'AVERAGEIF'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::AVERAGEIF',
                'argumentCount' => '2,3'
            ],
            'AVERAGEIFS'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '3+'
            ],
            'BAHTTEXT'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1'
            ],
            'BESSELI'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::BESSELI',
                'argumentCount' => '2'
            ],
            'BESSELJ'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::BESSELJ',
                'argumentCount' => '2'
            ],
            'BESSELK'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::BESSELK',
                'argumentCount' => '2'
            ],
            'BESSELY'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::BESSELY',
                'argumentCount' => '2'
            ],
            'BETADIST'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::BETADIST',
                'argumentCount' => '3-5'
            ],
            'BETAINV'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::BETAINV',
                'argumentCount' => '3-5'
            ],
            'BIN2DEC'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::BINTODEC',
                'argumentCount' => '1'
            ],
            'BIN2HEX'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::BINTOHEX',
                'argumentCount' => '1,2'
            ],
            'BIN2OCT'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::BINTOOCT',
                'argumentCount' => '1,2'
            ],
            'BINOMDIST'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::BINOMDIST',
                'argumentCount' => '4'
            ],
            'CEILING'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::CEILING',
                'argumentCount' => '2'
            ],
            'CELL'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1,2'
            ],
            'CHAR'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::CHARACTER',
                'argumentCount' => '1'
            ],
            'CHIDIST'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::CHIDIST',
                'argumentCount' => '2'
            ],
            'CHIINV'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::CHIINV',
                'argumentCount' => '2'
            ],
            'CHITEST'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2'
            ],
            'CHOOSE'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::CHOOSE',
                'argumentCount' => '2+'
            ],
            'CLEAN'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::TRIMNONPRINTABLE',
                'argumentCount' => '1'
            ],
            'CODE'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::ASCIICODE',
                'argumentCount' => '1'
            ],
            'COLUMN'             => [
                'category'        => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'    => 'PHPExcel_Calculation_LookupRef::COLUMN',
                'argumentCount'   => '-1',
                'passByReference' => [true]
            ],
            'COLUMNS'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::COLUMNS',
                'argumentCount' => '1'
            ],
            'COMBIN'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::COMBIN',
                'argumentCount' => '2'
            ],
            'COMPLEX'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::COMPLEX',
                'argumentCount' => '2,3'
            ],
            'CONCATENATE'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::CONCATENATE',
                'argumentCount' => '1+'
            ],
            'CONFIDENCE'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::CONFIDENCE',
                'argumentCount' => '3'
            ],
            'CONVERT'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::CONVERTUOM',
                'argumentCount' => '3'
            ],
            'CORREL'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::CORREL',
                'argumentCount' => '2'
            ],
            'COS'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'cos',
                'argumentCount' => '1'
            ],
            'COSH'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'cosh',
                'argumentCount' => '1'
            ],
            'COUNT'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::COUNT',
                'argumentCount' => '1+'
            ],
            'COUNTA'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::COUNTA',
                'argumentCount' => '1+'
            ],
            'COUNTBLANK'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::COUNTBLANK',
                'argumentCount' => '1'
            ],
            'COUNTIF'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::COUNTIF',
                'argumentCount' => '2'
            ],
            'COUNTIFS'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2'
            ],
            'COUPDAYBS'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::COUPDAYBS',
                'argumentCount' => '3,4'
            ],
            'COUPDAYS'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::COUPDAYS',
                'argumentCount' => '3,4'
            ],
            'COUPDAYSNC'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::COUPDAYSNC',
                'argumentCount' => '3,4'
            ],
            'COUPNCD'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::COUPNCD',
                'argumentCount' => '3,4'
            ],
            'COUPNUM'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::COUPNUM',
                'argumentCount' => '3,4'
            ],
            'COUPPCD'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::COUPPCD',
                'argumentCount' => '3,4'
            ],
            'COVAR'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::COVAR',
                'argumentCount' => '2'
            ],
            'CRITBINOM'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::CRITBINOM',
                'argumentCount' => '3'
            ],
            'CUBEKPIMEMBER'      => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_CUBE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '?'
            ],
            'CUBEMEMBER'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_CUBE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '?'
            ],
            'CUBEMEMBERPROPERTY' => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_CUBE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '?'
            ],
            'CUBERANKEDMEMBER'   => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_CUBE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '?'
            ],
            'CUBESET'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_CUBE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '?'
            ],
            'CUBESETCOUNT'       => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_CUBE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '?'
            ],
            'CUBEVALUE'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_CUBE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '?'
            ],
            'CUMIPMT'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::CUMIPMT',
                'argumentCount' => '6'
            ],
            'CUMPRINC'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::CUMPRINC',
                'argumentCount' => '6'
            ],
            'DATE'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DATE',
                'argumentCount' => '3'
            ],
            'DATEDIF'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DATEDIF',
                'argumentCount' => '2,3'
            ],
            'DATEVALUE'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DATEVALUE',
                'argumentCount' => '1'
            ],
            'DAVERAGE'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DAVERAGE',
                'argumentCount' => '3'
            ],
            'DAY'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DAYOFMONTH',
                'argumentCount' => '1'
            ],
            'DAYS360'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DAYS360',
                'argumentCount' => '2,3'
            ],
            'DB'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::DB',
                'argumentCount' => '4,5'
            ],
            'DCOUNT'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DCOUNT',
                'argumentCount' => '3'
            ],
            'DCOUNTA'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DCOUNTA',
                'argumentCount' => '3'
            ],
            'DDB'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::DDB',
                'argumentCount' => '4,5'
            ],
            'DEC2BIN'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::DECTOBIN',
                'argumentCount' => '1,2'
            ],
            'DEC2HEX'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::DECTOHEX',
                'argumentCount' => '1,2'
            ],
            'DEC2OCT'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::DECTOOCT',
                'argumentCount' => '1,2'
            ],
            'DEGREES'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'rad2deg',
                'argumentCount' => '1'
            ],
            'DELTA'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::DELTA',
                'argumentCount' => '1,2'
            ],
            'DEVSQ'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::DEVSQ',
                'argumentCount' => '1+'
            ],
            'DGET'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DGET',
                'argumentCount' => '3'
            ],
            'DISC'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::DISC',
                'argumentCount' => '4,5'
            ],
            'DMAX'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DMAX',
                'argumentCount' => '3'
            ],
            'DMIN'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DMIN',
                'argumentCount' => '3'
            ],
            'DOLLAR'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::DOLLAR',
                'argumentCount' => '1,2'
            ],
            'DOLLARDE'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::DOLLARDE',
                'argumentCount' => '2'
            ],
            'DOLLARFR'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::DOLLARFR',
                'argumentCount' => '2'
            ],
            'DPRODUCT'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DPRODUCT',
                'argumentCount' => '3'
            ],
            'DSTDEV'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DSTDEV',
                'argumentCount' => '3'
            ],
            'DSTDEVP'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DSTDEVP',
                'argumentCount' => '3'
            ],
            'DSUM'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DSUM',
                'argumentCount' => '3'
            ],
            'DURATION'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '5,6'
            ],
            'DVAR'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DVAR',
                'argumentCount' => '3'
            ],
            'DVARP'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATABASE,
                'functionCall'  => 'PHPExcel_Calculation_Database::DVARP',
                'argumentCount' => '3'
            ],
            'EDATE'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::EDATE',
                'argumentCount' => '2'
            ],
            'EFFECT'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::EFFECT',
                'argumentCount' => '2'
            ],
            'EOMONTH'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::EOMONTH',
                'argumentCount' => '2'
            ],
            'ERF'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::ERF',
                'argumentCount' => '1,2'
            ],
            'ERFC'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::ERFC',
                'argumentCount' => '1'
            ],
            'ERROR.TYPE'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::ERROR_TYPE',
                'argumentCount' => '1'
            ],
            'EVEN'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::EVEN',
                'argumentCount' => '1'
            ],
            'EXACT'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2'
            ],
            'EXP'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'exp',
                'argumentCount' => '1'
            ],
            'EXPONDIST'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::EXPONDIST',
                'argumentCount' => '3'
            ],
            'FACT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::FACT',
                'argumentCount' => '1'
            ],
            'FACTDOUBLE'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::FACTDOUBLE',
                'argumentCount' => '1'
            ],
            'FALSE'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                'functionCall'  => 'PHPExcel_Calculation_Logical::FALSE',
                'argumentCount' => '0'
            ],
            'FDIST'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '3'
            ],
            'FIND'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::SEARCHSENSITIVE',
                'argumentCount' => '2,3'
            ],
            'FINDB'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::SEARCHSENSITIVE',
                'argumentCount' => '2,3'
            ],
            'FINV'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '3'
            ],
            'FISHER'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::FISHER',
                'argumentCount' => '1'
            ],
            'FISHERINV'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::FISHERINV',
                'argumentCount' => '1'
            ],
            'FIXED'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::FIXEDFORMAT',
                'argumentCount' => '1-3'
            ],
            'FLOOR'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::FLOOR',
                'argumentCount' => '2'
            ],
            'FORECAST'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::FORECAST',
                'argumentCount' => '3'
            ],
            'FREQUENCY'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2'
            ],
            'FTEST'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2'
            ],
            'FV'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::FV',
                'argumentCount' => '3-5'
            ],
            'FVSCHEDULE'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::FVSCHEDULE',
                'argumentCount' => '2'
            ],
            'GAMMADIST'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::GAMMADIST',
                'argumentCount' => '4'
            ],
            'GAMMAINV'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::GAMMAINV',
                'argumentCount' => '3'
            ],
            'GAMMALN'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::GAMMALN',
                'argumentCount' => '1'
            ],
            'GCD'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::GCD',
                'argumentCount' => '1+'
            ],
            'GEOMEAN'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::GEOMEAN',
                'argumentCount' => '1+'
            ],
            'GESTEP'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::GESTEP',
                'argumentCount' => '1,2'
            ],
            'GETPIVOTDATA'       => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2+'
            ],
            'GROWTH'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::GROWTH',
                'argumentCount' => '1-4'
            ],
            'HARMEAN'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::HARMEAN',
                'argumentCount' => '1+'
            ],
            'HEX2BIN'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::HEXTOBIN',
                'argumentCount' => '1,2'
            ],
            'HEX2DEC'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::HEXTODEC',
                'argumentCount' => '1'
            ],
            'HEX2OCT'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::HEXTOOCT',
                'argumentCount' => '1,2'
            ],
            'HLOOKUP'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::HLOOKUP',
                'argumentCount' => '3,4'
            ],
            'HOUR'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::HOUROFDAY',
                'argumentCount' => '1'
            ],
            'HYPERLINK'          => [
                'category'          => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'      => 'PHPExcel_Calculation_LookupRef::HYPERLINK',
                'argumentCount'     => '1,2',
                'passCellReference' => true
            ],
            'HYPGEOMDIST'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::HYPGEOMDIST',
                'argumentCount' => '4'
            ],
            'IF'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                'functionCall'  => 'PHPExcel_Calculation_Logical::STATEMENT_IF',
                'argumentCount' => '1-3'
            ],
            'IFERROR'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                'functionCall'  => 'PHPExcel_Calculation_Logical::IFERROR',
                'argumentCount' => '2'
            ],
            'IMABS'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMABS',
                'argumentCount' => '1'
            ],
            'IMAGINARY'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMAGINARY',
                'argumentCount' => '1'
            ],
            'IMARGUMENT'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMARGUMENT',
                'argumentCount' => '1'
            ],
            'IMCONJUGATE'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMCONJUGATE',
                'argumentCount' => '1'
            ],
            'IMCOS'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMCOS',
                'argumentCount' => '1'
            ],
            'IMDIV'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMDIV',
                'argumentCount' => '2'
            ],
            'IMEXP'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMEXP',
                'argumentCount' => '1'
            ],
            'IMLN'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMLN',
                'argumentCount' => '1'
            ],
            'IMLOG10'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMLOG10',
                'argumentCount' => '1'
            ],
            'IMLOG2'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMLOG2',
                'argumentCount' => '1'
            ],
            'IMPOWER'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMPOWER',
                'argumentCount' => '2'
            ],
            'IMPRODUCT'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMPRODUCT',
                'argumentCount' => '1+'
            ],
            'IMREAL'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMREAL',
                'argumentCount' => '1'
            ],
            'IMSIN'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMSIN',
                'argumentCount' => '1'
            ],
            'IMSQRT'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMSQRT',
                'argumentCount' => '1'
            ],
            'IMSUB'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMSUB',
                'argumentCount' => '2'
            ],
            'IMSUM'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::IMSUM',
                'argumentCount' => '1+'
            ],
            'INDEX'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::INDEX',
                'argumentCount' => '1-4'
            ],
            'INDIRECT'           => [
                'category'          => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'      => 'PHPExcel_Calculation_LookupRef::INDIRECT',
                'argumentCount'     => '1,2',
                'passCellReference' => true
            ],
            'INFO'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1'
            ],
            'INT'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::INT',
                'argumentCount' => '1'
            ],
            'INTERCEPT'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::INTERCEPT',
                'argumentCount' => '2'
            ],
            'INTRATE'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::INTRATE',
                'argumentCount' => '4,5'
            ],
            'IPMT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::IPMT',
                'argumentCount' => '4-6'
            ],
            'IRR'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::IRR',
                'argumentCount' => '1,2'
            ],
            'ISBLANK'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_BLANK',
                'argumentCount' => '1'
            ],
            'ISERR'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_ERR',
                'argumentCount' => '1'
            ],
            'ISERROR'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_ERROR',
                'argumentCount' => '1'
            ],
            'ISEVEN'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_EVEN',
                'argumentCount' => '1'
            ],
            'ISLOGICAL'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_LOGICAL',
                'argumentCount' => '1'
            ],
            'ISNA'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_NA',
                'argumentCount' => '1'
            ],
            'ISNONTEXT'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_NONTEXT',
                'argumentCount' => '1'
            ],
            'ISNUMBER'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_NUMBER',
                'argumentCount' => '1'
            ],
            'ISODD'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_ODD',
                'argumentCount' => '1'
            ],
            'ISPMT'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::ISPMT',
                'argumentCount' => '4'
            ],
            'ISREF'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1'
            ],
            'ISTEXT'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::IS_TEXT',
                'argumentCount' => '1'
            ],
            'JIS'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1'
            ],
            'KURT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::KURT',
                'argumentCount' => '1+'
            ],
            'LARGE'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::LARGE',
                'argumentCount' => '2'
            ],
            'LCM'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::LCM',
                'argumentCount' => '1+'
            ],
            'LEFT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::LEFT',
                'argumentCount' => '1,2'
            ],
            'LEFTB'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::LEFT',
                'argumentCount' => '1,2'
            ],
            'LEN'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::STRINGLENGTH',
                'argumentCount' => '1'
            ],
            'LENB'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::STRINGLENGTH',
                'argumentCount' => '1'
            ],
            'LINEST'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::LINEST',
                'argumentCount' => '1-4'
            ],
            'LN'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'log',
                'argumentCount' => '1'
            ],
            'LOG'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::LOG_BASE',
                'argumentCount' => '1,2'
            ],
            'LOG10'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'log10',
                'argumentCount' => '1'
            ],
            'LOGEST'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::LOGEST',
                'argumentCount' => '1-4'
            ],
            'LOGINV'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::LOGINV',
                'argumentCount' => '3'
            ],
            'LOGNORMDIST'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::LOGNORMDIST',
                'argumentCount' => '3'
            ],
            'LOOKUP'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::LOOKUP',
                'argumentCount' => '2,3'
            ],
            'LOWER'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::LOWERCASE',
                'argumentCount' => '1'
            ],
            'MATCH'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::MATCH',
                'argumentCount' => '2,3'
            ],
            'MAX'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MAX',
                'argumentCount' => '1+'
            ],
            'MAXA'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MAXA',
                'argumentCount' => '1+'
            ],
            'MAXIF'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MAXIF',
                'argumentCount' => '2+'
            ],
            'MDETERM'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::MDETERM',
                'argumentCount' => '1'
            ],
            'MDURATION'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '5,6'
            ],
            'MEDIAN'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MEDIAN',
                'argumentCount' => '1+'
            ],
            'MEDIANIF'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2+'
            ],
            'MID'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::MID',
                'argumentCount' => '3'
            ],
            'MIDB'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::MID',
                'argumentCount' => '3'
            ],
            'MIN'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MIN',
                'argumentCount' => '1+'
            ],
            'MINA'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MINA',
                'argumentCount' => '1+'
            ],
            'MINIF'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MINIF',
                'argumentCount' => '2+'
            ],
            'MINUTE'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::MINUTEOFHOUR',
                'argumentCount' => '1'
            ],
            'MINVERSE'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::MINVERSE',
                'argumentCount' => '1'
            ],
            'MIRR'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::MIRR',
                'argumentCount' => '3'
            ],
            'MMULT'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::MMULT',
                'argumentCount' => '2'
            ],
            'MOD'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::MOD',
                'argumentCount' => '2'
            ],
            'MODE'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::MODE',
                'argumentCount' => '1+'
            ],
            'MONTH'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::MONTHOFYEAR',
                'argumentCount' => '1'
            ],
            'MROUND'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::MROUND',
                'argumentCount' => '2'
            ],
            'MULTINOMIAL'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::MULTINOMIAL',
                'argumentCount' => '1+'
            ],
            'N'                  => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::N',
                'argumentCount' => '1'
            ],
            'NA'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::NA',
                'argumentCount' => '0'
            ],
            'NEGBINOMDIST'       => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::NEGBINOMDIST',
                'argumentCount' => '3'
            ],
            'NETWORKDAYS'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::NETWORKDAYS',
                'argumentCount' => '2+'
            ],
            'NOMINAL'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::NOMINAL',
                'argumentCount' => '2'
            ],
            'NORMDIST'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::NORMDIST',
                'argumentCount' => '4'
            ],
            'NORMINV'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::NORMINV',
                'argumentCount' => '3'
            ],
            'NORMSDIST'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::NORMSDIST',
                'argumentCount' => '1'
            ],
            'NORMSINV'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::NORMSINV',
                'argumentCount' => '1'
            ],
            'NOT'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                'functionCall'  => 'PHPExcel_Calculation_Logical::NOT',
                'argumentCount' => '1'
            ],
            'NOW'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DATETIMENOW',
                'argumentCount' => '0'
            ],
            'NPER'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::NPER',
                'argumentCount' => '3-5'
            ],
            'NPV'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::NPV',
                'argumentCount' => '2+'
            ],
            'OCT2BIN'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::OCTTOBIN',
                'argumentCount' => '1,2'
            ],
            'OCT2DEC'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::OCTTODEC',
                'argumentCount' => '1'
            ],
            'OCT2HEX'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_ENGINEERING,
                'functionCall'  => 'PHPExcel_Calculation_Engineering::OCTTOHEX',
                'argumentCount' => '1,2'
            ],
            'ODD'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::ODD',
                'argumentCount' => '1'
            ],
            'ODDFPRICE'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '8,9'
            ],
            'ODDFYIELD'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '8,9'
            ],
            'ODDLPRICE'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '7,8'
            ],
            'ODDLYIELD'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '7,8'
            ],
            'OFFSET'             => [
                'category'          => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'      => 'PHPExcel_Calculation_LookupRef::OFFSET',
                'argumentCount'     => '3-5',
                'passCellReference' => true,
                'passByReference'   => [true]
            ],
            'OR'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                'functionCall'  => 'PHPExcel_Calculation_Logical::LOGICAL_OR',
                'argumentCount' => '1+'
            ],
            'PEARSON'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::CORREL',
                'argumentCount' => '2'
            ],
            'PERCENTILE'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::PERCENTILE',
                'argumentCount' => '2'
            ],
            'PERCENTRANK'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::PERCENTRANK',
                'argumentCount' => '2,3'
            ],
            'PERMUT'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::PERMUT',
                'argumentCount' => '2'
            ],
            'PHONETIC'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1'
            ],
            'PI'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'pi',
                'argumentCount' => '0'
            ],
            'PMT'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::PMT',
                'argumentCount' => '3-5'
            ],
            'POISSON'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::POISSON',
                'argumentCount' => '3'
            ],
            'POWER'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::POWER',
                'argumentCount' => '2'
            ],
            'PPMT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::PPMT',
                'argumentCount' => '4-6'
            ],
            'PRICE'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::PRICE',
                'argumentCount' => '6,7'
            ],
            'PRICEDISC'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::PRICEDISC',
                'argumentCount' => '4,5'
            ],
            'PRICEMAT'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::PRICEMAT',
                'argumentCount' => '5,6'
            ],
            'PROB'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '3,4'
            ],
            'PRODUCT'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::PRODUCT',
                'argumentCount' => '1+'
            ],
            'PROPER'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::PROPERCASE',
                'argumentCount' => '1'
            ],
            'PV'                 => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::PV',
                'argumentCount' => '3-5'
            ],
            'QUARTILE'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::QUARTILE',
                'argumentCount' => '2'
            ],
            'QUOTIENT'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::QUOTIENT',
                'argumentCount' => '2'
            ],
            'RADIANS'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'deg2rad',
                'argumentCount' => '1'
            ],
            'RAND'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::RAND',
                'argumentCount' => '0'
            ],
            'RANDBETWEEN'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::RAND',
                'argumentCount' => '2'
            ],
            'RANK'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::RANK',
                'argumentCount' => '2,3'
            ],
            'RATE'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::RATE',
                'argumentCount' => '3-6'
            ],
            'RECEIVED'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::RECEIVED',
                'argumentCount' => '4-5'
            ],
            'REPLACE'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::REPLACE',
                'argumentCount' => '4'
            ],
            'REPLACEB'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::REPLACE',
                'argumentCount' => '4'
            ],
            'REPT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'str_repeat',
                'argumentCount' => '2'
            ],
            'RIGHT'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::RIGHT',
                'argumentCount' => '1,2'
            ],
            'RIGHTB'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::RIGHT',
                'argumentCount' => '1,2'
            ],
            'ROMAN'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::ROMAN',
                'argumentCount' => '1,2'
            ],
            'ROUND'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'round',
                'argumentCount' => '2'
            ],
            'ROUNDDOWN'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::ROUNDDOWN',
                'argumentCount' => '2'
            ],
            'ROUNDUP'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::ROUNDUP',
                'argumentCount' => '2'
            ],
            'ROW'                => [
                'category'        => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'    => 'PHPExcel_Calculation_LookupRef::ROW',
                'argumentCount'   => '-1',
                'passByReference' => [true]
            ],
            'ROWS'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::ROWS',
                'argumentCount' => '1'
            ],
            'RSQ'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::RSQ',
                'argumentCount' => '2'
            ],
            'RTD'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '1+'
            ],
            'SEARCH'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::SEARCHINSENSITIVE',
                'argumentCount' => '2,3'
            ],
            'SEARCHB'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::SEARCHINSENSITIVE',
                'argumentCount' => '2,3'
            ],
            'SECOND'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::SECONDOFMINUTE',
                'argumentCount' => '1'
            ],
            'SERIESSUM'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SERIESSUM',
                'argumentCount' => '4'
            ],
            'SIGN'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SIGN',
                'argumentCount' => '1'
            ],
            'SIN'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'sin',
                'argumentCount' => '1'
            ],
            'SINH'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'sinh',
                'argumentCount' => '1'
            ],
            'SKEW'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::SKEW',
                'argumentCount' => '1+'
            ],
            'SLN'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::SLN',
                'argumentCount' => '3'
            ],
            'SLOPE'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::SLOPE',
                'argumentCount' => '2'
            ],
            'SMALL'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::SMALL',
                'argumentCount' => '2'
            ],
            'SQRT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'sqrt',
                'argumentCount' => '1'
            ],
            'SQRTPI'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SQRTPI',
                'argumentCount' => '1'
            ],
            'STANDARDIZE'        => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::STANDARDIZE',
                'argumentCount' => '3'
            ],
            'STDEV'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::STDEV',
                'argumentCount' => '1+'
            ],
            'STDEVA'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::STDEVA',
                'argumentCount' => '1+'
            ],
            'STDEVP'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::STDEVP',
                'argumentCount' => '1+'
            ],
            'STDEVPA'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::STDEVPA',
                'argumentCount' => '1+'
            ],
            'STEYX'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::STEYX',
                'argumentCount' => '2'
            ],
            'SUBSTITUTE'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::SUBSTITUTE',
                'argumentCount' => '3,4'
            ],
            'SUBTOTAL'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUBTOTAL',
                'argumentCount' => '2+'
            ],
            'SUM'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUM',
                'argumentCount' => '1+'
            ],
            'SUMIF'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUMIF',
                'argumentCount' => '2,3'
            ],
            'SUMIFS'             => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUMIFS',
                'argumentCount' => '3+'
            ],
            'SUMPRODUCT'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUMPRODUCT',
                'argumentCount' => '1+'
            ],
            'SUMSQ'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUMSQ',
                'argumentCount' => '1+'
            ],
            'SUMX2MY2'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUMX2MY2',
                'argumentCount' => '2'
            ],
            'SUMX2PY2'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUMX2PY2',
                'argumentCount' => '2'
            ],
            'SUMXMY2'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::SUMXMY2',
                'argumentCount' => '2'
            ],
            'SYD'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::SYD',
                'argumentCount' => '4'
            ],
            'T'                  => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::RETURNSTRING',
                'argumentCount' => '1'
            ],
            'TAN'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'tan',
                'argumentCount' => '1'
            ],
            'TANH'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'tanh',
                'argumentCount' => '1'
            ],
            'TBILLEQ'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::TBILLEQ',
                'argumentCount' => '3'
            ],
            'TBILLPRICE'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::TBILLPRICE',
                'argumentCount' => '3'
            ],
            'TBILLYIELD'         => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::TBILLYIELD',
                'argumentCount' => '3'
            ],
            'TDIST'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::TDIST',
                'argumentCount' => '3'
            ],
            'TEXT'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::TEXTFORMAT',
                'argumentCount' => '2'
            ],
            'TIME'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::TIME',
                'argumentCount' => '3'
            ],
            'TIMEVALUE'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::TIMEVALUE',
                'argumentCount' => '1'
            ],
            'TINV'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::TINV',
                'argumentCount' => '2'
            ],
            'TODAY'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DATENOW',
                'argumentCount' => '0'
            ],
            'TRANSPOSE'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::TRANSPOSE',
                'argumentCount' => '1'
            ],
            'TREND'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::TREND',
                'argumentCount' => '1-4'
            ],
            'TRIM'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::TRIMSPACES',
                'argumentCount' => '1'
            ],
            'TRIMMEAN'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::TRIMMEAN',
                'argumentCount' => '2'
            ],
            'TRUE'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOGICAL,
                'functionCall'  => 'PHPExcel_Calculation_Logical::TRUE',
                'argumentCount' => '0'
            ],
            'TRUNC'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_MATH_AND_TRIG,
                'functionCall'  => 'PHPExcel_Calculation_MathTrig::TRUNC',
                'argumentCount' => '1,2'
            ],
            'TTEST'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '4'
            ],
            'TYPE'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::TYPE',
                'argumentCount' => '1'
            ],
            'UPPER'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::UPPERCASE',
                'argumentCount' => '1'
            ],
            'USDOLLAR'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '2'
            ],
            'VALUE'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_TEXT_AND_DATA,
                'functionCall'  => 'PHPExcel_Calculation_TextData::VALUE',
                'argumentCount' => '1'
            ],
            'VAR'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::VARFunc',
                'argumentCount' => '1+'
            ],
            'VARA'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::VARA',
                'argumentCount' => '1+'
            ],
            'VARP'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::VARP',
                'argumentCount' => '1+'
            ],
            'VARPA'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::VARPA',
                'argumentCount' => '1+'
            ],
            'VDB'                => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '5-7'
            ],
            'VERSION'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_INFORMATION,
                'functionCall'  => 'PHPExcel_Calculation_Functions::VERSION',
                'argumentCount' => '0'
            ],
            'VLOOKUP'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_LOOKUP_AND_REFERENCE,
                'functionCall'  => 'PHPExcel_Calculation_LookupRef::VLOOKUP',
                'argumentCount' => '3,4'
            ],
            'WEEKDAY'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::DAYOFWEEK',
                'argumentCount' => '1,2'
            ],
            'WEEKNUM'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::WEEKOFYEAR',
                'argumentCount' => '1,2'
            ],
            'WEIBULL'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::WEIBULL',
                'argumentCount' => '4'
            ],
            'WORKDAY'            => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::WORKDAY',
                'argumentCount' => '2+'
            ],
            'XIRR'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::XIRR',
                'argumentCount' => '2,3'
            ],
            'XNPV'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::XNPV',
                'argumentCount' => '3'
            ],
            'YEAR'               => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::YEAR',
                'argumentCount' => '1'
            ],
            'YEARFRAC'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_DATE_AND_TIME,
                'functionCall'  => 'PHPExcel_Calculation_DateTime::YEARFRAC',
                'argumentCount' => '2,3'
            ],
            'YIELD'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Functions::DUMMY',
                'argumentCount' => '6,7'
            ],
            'YIELDDISC'          => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::YIELDDISC',
                'argumentCount' => '4,5'
            ],
            'YIELDMAT'           => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_FINANCIAL,
                'functionCall'  => 'PHPExcel_Calculation_Financial::YIELDMAT',
                'argumentCount' => '5,6'
            ],
            'ZTEST'              => [
                'category'      => PHPExcel_Calculation_Function::CATEGORY_STATISTICAL,
                'functionCall'  => 'PHPExcel_Calculation_Statistical::ZTEST',
                'argumentCount' => '2-3'
            ]
        ];
        private static $controlFunctions          = [
            'MKMATRIX' => [
                'argumentCount' => '*',
                'functionCall'  => 'self::mkMatrix'
            ]
        ];
        private static $functionReplaceFromExcel  = null;
        private static $functionReplaceToLocale   = null;
        private static $functionReplaceFromLocale = null;
        private static $functionReplaceToExcel    = null;
        private static $operatorAssociativity     = [
            '^'  => 0,
            //    Exponentiation
            '*'  => 0,
            '/'  => 0,
            //    Multiplication and Division
            '+'  => 0,
            '-'  => 0,
            //    Addition and Subtraction
            '&'  => 0,
            //    Concatenation
            '|'  => 0,
            ':'  => 0,
            //    Intersect and Range
            '>'  => 0,
            '<'  => 0,
            '='  => 0,
            '>=' => 0,
            '<=' => 0,
            '<>' => 0
            //    Comparison
        ];                    //    US English    (default locale)
        private static $comparisonOperators       = [
            '>'  => true,
            '<'  => true,
            '='  => true,
            '>=' => true,
            '<=' => true,
            '<>' => true
        ];
        private static $operatorPrecedence        = [
            ':'  => 8,
            //    Range
            '|'  => 7,
            //    Intersect
            '~'  => 6,
            //    Negation
            '%'  => 5,
            //    Percentage
            '^'  => 4,
            //    Exponentiation
            '*'  => 3,
            '/'  => 3,
            //    Multiplication and Division
            '+'  => 2,
            '-'  => 2,
            //    Addition and Subtraction
            '&'  => 1,
            //    Concatenation
            '>'  => 0,
            '<'  => 0,
            '='  => 0,
            '>=' => 0,
            '<=' => 0,
            '<>' => 0
            //    Comparison
        ];
        /**
         * Flag to determine how formula errors should be handled
         *        If true, then a user error will be triggered
         *        If false, then an exception will be thrown
         * @access    public
         * @var boolean
         */
        public $suppressFormulaErrors = false;
        /**
         * Error message for any error that was raised/thrown by the calculation engine
         * @access    public
         * @var string
         */
        public $formulaError = null;
        /**
         * Number of iterations for cyclic formulae
         * @var integer
         */
        public $cyclicFormulaCount = 1;
        //    PHPExcel functions
        /**
         * Instance of the workbook this Calculation Engine is using
         * @access    private
         * @var PHPExcel
         */
        private $workbook;
        //    Internal functions used for special control purposes
        /**
         * Calculation cache
         * @access    private
         * @var array
         */
        private $calculationCache = [];
        /**
         * Calculation cache enabled
         * @access    private
         * @var boolean
         */
        private $calculationCacheEnabled = true;
        /**
         * The debug log generated by the calculation engine
         * @access    private
         * @var PHPExcel_CalcEngine_Logger
         */
        private $debugLog;
        /**
         * An array of the nested cell references accessed by the calculation engine, used for the debug log
         * @access    private
         * @var array of string
         */
        private $cyclicReferenceStack;
        private $cellStack = [];
        /**
         * Current iteration counter for cyclic formulae
         * If the value is 0 (or less) then cyclic formulae will throw an exception,
         *    otherwise they will iterate to the limit defined here before returning a result
         * @var integer
         */
        private $cyclicFormulaCounter = 1;
        private $cyclicFormulaCell    = '';
        /**
         * Epsilon Precision used for comparisons in calculations
         * @var float
         */
        private $delta = 0.1e-12;

        public function __construct(PHPExcel $workbook = null) {
            $this->delta = 1 * pow(10, 0 - ini_get('precision'));
            $this->workbook             = $workbook;
            $this->cyclicReferenceStack = new PHPExcel_CalcEngine_CyclicReferenceStack();
            $this->_debugLog            = new PHPExcel_CalcEngine_Logger($this->cyclicReferenceStack);
        }

        /**
         * Get an instance of this class
         * @access    public
         * @param   PHPExcel $workbook        Injected workbook for working with a PHPExcel object,
         *                                    or NULL to create a standalone claculation engine
         * @return PHPExcel_Calculation
         */
        public static function getInstance(PHPExcel $workbook = null) {
            if ($workbook !== null) {
                $instance = $workbook->getCalculationEngine();
                if (isset($instance)) {
                    return $instance;
                }
            }
            if (!isset(self::$instance) || (self::$instance === null)) {
                self::$instance = new PHPExcel_Calculation();
            }
            return self::$instance;
        }

        /**
         * Return the locale-specific translation of TRUE
         * @access    public
         * @return     string        locale-specific translation of TRUE
         */
        public static function getTRUE() {
            return self::$localeBoolean['TRUE'];
        }

        /**
         * Return the locale-specific translation of FALSE
         * @access    public
         * @return     string        locale-specific translation of FALSE
         */
        public static function getFALSE() {
            return self::$localeBoolean['FALSE'];
        }

        /**
         * Set the Array Return Type (Array or Value of first element in the array)
         * @access    public
         * @param     string $returnType Array return type
         * @return     boolean                    Success or failure
         */
        public static function setArrayReturnType($returnType) {
            if (($returnType == self::RETURN_ARRAY_AS_VALUE) || ($returnType == self::RETURN_ARRAY_AS_ERROR) || ($returnType == self::RETURN_ARRAY_AS_ARRAY)) {
                self::$returnArrayAsType = $returnType;
                return true;
            }
            return false;
        }

        /**
         * Return the Array Return Type (Array or Value of first element in the array)
         * @access    public
         * @return     string        $returnType            Array return type
         */
        public static function getArrayReturnType() {
            return self::$returnArrayAsType;
        }

        private static function mkMatrix() {
            return func_get_args();
        }

        /**
         * Unset an instance of this class
         * @access    public
         */
        public function __destruct() {
            $this->workbook = null;
        }

        /**
         * Flush the calculation cache for any existing instance of this class
         *        but only if a PHPExcel_Calculation instance exists
         * @access    public
         * @return null
         */
        public function flushInstance() {
            $this->clearCalculationCache();
        }

        /**
         * Clear calculation cache
         */
        public function clearCalculationCache() {
            $this->calculationCache = [];
        }

        /**
         * Get the debuglog for this claculation engine instance
         * @access    public
         * @return PHPExcel_CalcEngine_Logger
         */
        public function getDebugLog() {
            return $this->_debugLog;
        }

        /**
         * __clone implementation. Cloning should not be allowed in a Singleton!
         * @access    public
         * @throws    PHPExcel_Calculation_Exception
         */
        final public function __clone() {
            throw new PHPExcel_Calculation_Exception('Cloning the calculation engine is not allowed!');
        }

        /**
         * Enable calculation cache
         */
        public function enableCalculationCache() {
            $this->setCalculationCacheEnabled(true);
        }

        /**
         * Disable calculation cache
         */
        public function disableCalculationCache() {
            $this->setCalculationCacheEnabled(false);
        }

        /**
         * Clear calculation cache for a specified worksheet
         * @param string $worksheetName
         */
        public function clearCalculationCacheForWorksheet($worksheetName) {
            if (isset($this->calculationCache[$worksheetName])) {
                unset($this->calculationCache[$worksheetName]);
            }
        }

        /**
         * Rename calculation cache for a specified worksheet
         * @param string $fromWorksheetName
         * @param string $toWorksheetName
         */
        public function renameCalculationCacheForWorksheet($fromWorksheetName, $toWorksheetName) {
            if (isset($this->calculationCache[$fromWorksheetName])) {
                $this->calculationCache[$toWorksheetName] = &$this->calculationCache[$fromWorksheetName];
                unset($this->calculationCache[$fromWorksheetName]);
            }
        }

        /**
         * Get the currently defined locale code
         * @return string
         */
        public function getLocale() {
            return self::$localeLanguage;
        }

        /**
         * Set the locale code
         * @param string $locale The locale to use for formula translation
         * @return boolean
         */
        public function setLocale($locale = 'en_us') {
            //    Identify our locale and language
            $language = $locale = strtolower($locale);
            if (strpos($locale, '_') !== false) {
                list($language) = explode('_', $locale);
            }
            if (count(self::$validLocaleLanguages) == 1) {
                self::loadLocales();
            }
            //    Test whether we have any language data for this language (any locale)
            if (in_array($language, self::$validLocaleLanguages)) {
                //    initialise language/locale settings
                self::$localeFunctions         = [];
                self::$localeArgumentSeparator = ',';
                self::$localeBoolean           = [
                    'TRUE'  => 'TRUE',
                    'FALSE' => 'FALSE',
                    'NULL'  => 'NULL'
                ];
                //    Default is English, if user isn't requesting english, then read the necessary data from the locale files
                if ($locale != 'en_us') {
                    //    Search for a file with a list of function names for locale
                    $functionNamesFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . str_replace('_', DIRECTORY_SEPARATOR, $locale) . DIRECTORY_SEPARATOR . 'functions';
                    if (!file_exists($functionNamesFile)) {
                        //    If there isn't a locale specific function file, look for a language specific function file
                        $functionNamesFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . $language . DIRECTORY_SEPARATOR . 'functions';
                        if (!file_exists($functionNamesFile)) {
                            return false;
                        }
                    }
                    //    Retrieve the list of locale or language specific function names
                    $localeFunctions = file($functionNamesFile, FILE_IGNORE_NEW_LINES | FILE_SKIP_EMPTY_LINES);
                    foreach ($localeFunctions as $localeFunction) {
                        list($localeFunction) = explode('##', $localeFunction);    //    Strip out comments
                        if (strpos($localeFunction, '=') !== false) {
                            list($fName, $lfName) = explode('=', $localeFunction);
                            $fName  = trim($fName);
                            $lfName = trim($lfName);
                            if ((isset(self::$PHPExcelFunctions[$fName])) && ($lfName != '') && ($fName != $lfName)) {
                                self::$localeFunctions[$fName] = $lfName;
                            }
                        }
                    }
                    //    Default the TRUE and FALSE constants to the locale names of the TRUE() and FALSE() functions
                    if (isset(self::$localeFunctions['TRUE'])) {
                        self::$localeBoolean['TRUE'] = self::$localeFunctions['TRUE'];
                    }
                    if (isset(self::$localeFunctions['FALSE'])) {
                        self::$localeBoolean['FALSE'] = self::$localeFunctions['FALSE'];
                    }
                    $configFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . str_replace('_', DIRECTORY_SEPARATOR, $locale) . DIRECTORY_SEPARATOR . 'config';
                    if (!file_exists($configFile)) {
                        $configFile = PHPEXCEL_ROOT . 'PHPExcel' . DIRECTORY_SEPARATOR . 'locale' . DIRECTORY_SEPARATOR . $language . DIRECTORY_SEPARATOR . 'config';
                    }
                    if (file_exists($configFile)) {
                        $localeSettings = file($configFile, FILE_IGNORE_NEW_LINES | FILE_SKIP_EMPTY_LINES);
                        foreach ($localeSettings as $localeSetting) {
                            list($localeSetting) = explode('##', $localeSetting);    //    Strip out comments
                            if (strpos($localeSetting, '=') !== false) {
                                list($settingName, $settingValue) = explode('=', $localeSetting);
                                $settingName = strtoupper(trim($settingName));
                                switch ($settingName) {
                                    case 'ARGUMENTSEPARATOR':
                                        self::$localeArgumentSeparator = trim($settingValue);
                                        break;
                                }
                            }
                        }
                    }
                }
                self::$functionReplaceFromExcel = self::$functionReplaceToExcel = self::$functionReplaceFromLocale = self::$functionReplaceToLocale = null;
                self::$localeLanguage           = $locale;
                return true;
            }
            return false;
        }

        private static function loadLocales() {
            $localeFileDirectory = PHPEXCEL_ROOT . 'PHPExcel/locale/';
            foreach (glob($localeFileDirectory . '/*', GLOB_ONLYDIR) as $filename) {
                $filename = substr($filename, strlen($localeFileDirectory) + 1);
                if ($filename != 'en') {
                    self::$validLocaleLanguages[] = $filename;
                }
            }
        }

        public function _translateFormulaToLocale($formula) {
            if (self::$functionReplaceFromExcel === null) {
                self::$functionReplaceFromExcel = [];
                foreach (array_keys(self::$localeFunctions) as $excelFunctionName) {
                    self::$functionReplaceFromExcel[] = '/(@?[^\w\.])' . preg_quote($excelFunctionName) . '([\s]*\()/Ui';
                }
                foreach (array_keys(self::$localeBoolean) as $excelBoolean) {
                    self::$functionReplaceFromExcel[] = '/(@?[^\w\.])' . preg_quote($excelBoolean) . '([^\w\.])/Ui';
                }
            }
            if (self::$functionReplaceToLocale === null) {
                self::$functionReplaceToLocale = [];
                foreach (array_values(self::$localeFunctions) as $localeFunctionName) {
                    self::$functionReplaceToLocale[] = '$1' . trim($localeFunctionName) . '$2';
                }
                foreach (array_values(self::$localeBoolean) as $localeBoolean) {
                    self::$functionReplaceToLocale[] = '$1' . trim($localeBoolean) . '$2';
                }
            }
            return self::translateFormula(self::$functionReplaceFromExcel, self::$functionReplaceToLocale, $formula, ',', self::$localeArgumentSeparator);
        }

        private static function translateFormula($from, $to, $formula, $fromSeparator, $toSeparator) {
            //    Convert any Excel function names to the required language
            if (self::$localeLanguage !== 'en_us') {
                $inBraces = false;
                //    If there is the possibility of braces within a quoted string, then we don't treat those as matrix indicators
                if (strpos($formula, '"') !== false) {
                    //    So instead we skip replacing in any quoted strings by only replacing in every other array element after we've exploded
                    //        the formula
                    $temp = explode('"', $formula);
                    $i    = false;
                    foreach ($temp as &$value) {
                        //    Only count/replace in alternating array entries
                        if ($i = !$i) {
                            $value = preg_replace($from, $to, $value);
                            $value = self::translateSeparator($fromSeparator, $toSeparator, $value, $inBraces);
                        }
                    }
                    unset($value);
                    //    Then rebuild the formula string
                    $formula = implode('"', $temp);
                } else {
                    //    If there's no quoted strings, then we do a simple count/replace
                    $formula = preg_replace($from, $to, $formula);
                    $formula = self::translateSeparator($fromSeparator, $toSeparator, $formula, $inBraces);
                }
            }
            return $formula;
        }

        public static function translateSeparator($fromSeparator, $toSeparator, $formula, &$inBraces) {
            $strlen = mb_strlen($formula);
            for ($i = 0; $i < $strlen; ++$i) {
                $chr = mb_substr($formula, $i, 1);
                switch ($chr) {
                    case '{':
                        $inBraces = true;
                        break;
                    case '}':
                        $inBraces = false;
                        break;
                    case $fromSeparator:
                        if (!$inBraces) {
                            $formula = mb_substr($formula, 0, $i) . $toSeparator . mb_substr($formula, $i + 1);
                        }
                }
            }
            return $formula;
        }

        public function _translateFormulaToEnglish($formula) {
            if (self::$functionReplaceFromLocale === null) {
                self::$functionReplaceFromLocale = [];
                foreach (array_values(self::$localeFunctions) as $localeFunctionName) {
                    self::$functionReplaceFromLocale[] = '/(@?[^\w\.])' . preg_quote($localeFunctionName) . '([\s]*\()/Ui';
                }
                foreach (array_values(self::$localeBoolean) as $excelBoolean) {
                    self::$functionReplaceFromLocale[] = '/(@?[^\w\.])' . preg_quote($excelBoolean) . '([^\w\.])/Ui';
                }
            }
            if (self::$functionReplaceToExcel === null) {
                self::$functionReplaceToExcel = [];
                foreach (array_keys(self::$localeFunctions) as $excelFunctionName) {
                    self::$functionReplaceToExcel[] = '$1' . trim($excelFunctionName) . '$2';
                }
                foreach (array_keys(self::$localeBoolean) as $excelBoolean) {
                    self::$functionReplaceToExcel[] = '$1' . trim($excelBoolean) . '$2';
                }
            }
            return self::translateFormula(self::$functionReplaceFromLocale, self::$functionReplaceToExcel, $formula, self::$localeArgumentSeparator, ',');
        }

        /**
         * Calculate cell value (using formula from a cell ID)
         * Retained for backward compatibility
         * @access    public
         * @param    PHPExcel_Cell $pCell Cell to calculate
         * @return    mixed
         * @throws    PHPExcel_Calculation_Exception
         */
        public function calculate(PHPExcel_Cell $pCell = null) {
            try {
                return $this->calculateCellValue($pCell);
            } catch (PHPExcel_Exception $e) {
                throw new PHPExcel_Calculation_Exception($e->getMessage());
            }
        }

        /**
         * Calculate the value of a cell formula
         * @access    public
         * @param    PHPExcel_Cell $pCell    Cell to calculate
         * @param    Boolean       $resetLog Flag indicating whether the debug log should be reset or not
         * @return    mixed
         * @throws    PHPExcel_Calculation_Exception
         */
        public function calculateCellValue(PHPExcel_Cell $pCell = null, $resetLog = true) {
            if ($pCell === null) {
                return null;
            }
            $returnArrayAsType = self::$returnArrayAsType;
            if ($resetLog) {
                //    Initialise the logging settings if requested
                $this->formulaError = null;
                $this->_debugLog->clearLog();
                $this->cyclicReferenceStack->clear();
                $this->cyclicFormulaCounter = 1;
                self::$returnArrayAsType = self::RETURN_ARRAY_AS_ARRAY;
            }
            //    Execute the calculation for the cell formula
            $this->cellStack[] = [
                'sheet' => $pCell->getWorksheet()->getTitle(),
                'cell'  => $pCell->getCoordinate(),
            ];
            try {
                $result      = self::unwrapResult($this->_calculateFormulaValue($pCell->getValue(), $pCell->getCoordinate(), $pCell));
                $cellAddress = array_pop($this->cellStack);
                $this->workbook->getSheetByName($cellAddress['sheet'])->getCell($cellAddress['cell']);
            } catch (PHPExcel_Exception $e) {
                $cellAddress = array_pop($this->cellStack);
                $this->workbook->getSheetByName($cellAddress['sheet'])->getCell($cellAddress['cell']);
                throw new PHPExcel_Calculation_Exception($e->getMessage());
            }
            if ((is_array($result)) && (self::$returnArrayAsType != self::RETURN_ARRAY_AS_ARRAY)) {
                self::$returnArrayAsType = $returnArrayAsType;
                $testResult              = PHPExcel_Calculation_Functions::flattenArray($result);
                if (self::$returnArrayAsType == self::RETURN_ARRAY_AS_ERROR) {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
                //    If there's only a single cell in the array, then we allow it
                if (count($testResult) != 1) {
                    //    If keys are numeric, then it's a matrix result rather than a cell range result, so we permit it
                    $r = array_keys($result);
                    $r = array_shift($r);
                    if (!is_numeric($r)) {
                        return PHPExcel_Calculation_Functions::VALUE();
                    }
                    if (is_array($result[$r])) {
                        $c = array_keys($result[$r]);
                        $c = array_shift($c);
                        if (!is_numeric($c)) {
                            return PHPExcel_Calculation_Functions::VALUE();
                        }
                    }
                }
                $result = array_shift($testResult);
            }
            self::$returnArrayAsType = $returnArrayAsType;
            if ($result === null) {
                return 0;
            } elseif ((is_float($result)) && ((is_nan($result)) || (is_infinite($result)))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return $result;
        }

        /**
         * Remove quotes used as a wrapper to identify string values
         * @param mixed $value
         * @return mixed
         */
        public static function unwrapResult($value) {
            if (is_string($value)) {
                if ((isset($value{0})) && ($value{0} == '"') && (substr($value, -1) == '"')) {
                    return substr($value, 1, -1);
                }
                //    Convert numeric errors to NaN error
            } elseif ((is_float($value)) && ((is_nan($value)) || (is_infinite($value)))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return $value;
        }

        /**
         * Parse a cell formula and calculate its value
         * @param    string        $formula The formula to parse and calculate
         * @param    string        $cellID  The ID (e.g. A3) of the cell that we are calculating
         * @param    PHPExcel_Cell $pCell   Cell to calculate
         * @return    mixed
         * @throws    PHPExcel_Calculation_Exception
         */
        public function _calculateFormulaValue($formula, $cellID = null, PHPExcel_Cell $pCell = null) {
            $cellValue = null;
            //    Basic validation that this is indeed a formula
            //    We simply return the cell value if not
            $formula = trim($formula);
            if ($formula{0} != '=') {
                return self::wrapResult($formula);
            }
            $formula = ltrim(substr($formula, 1));
            if (!isset($formula{0})) {
                return self::wrapResult($formula);
            }
            $pCellParent     = ($pCell !== null) ? $pCell->getWorksheet() : null;
            $wsTitle         = ($pCellParent !== null) ? $pCellParent->getTitle() : "\x00Wrk";
            $wsCellReference = $wsTitle . '!' . $cellID;
            if (($cellID !== null) && ($this->getValueFromCache($wsCellReference, $cellValue))) {
                return $cellValue;
            }
            if (($wsTitle{0} !== "\x00") && ($this->cyclicReferenceStack->onStack($wsCellReference))) {
                if ($this->cyclicFormulaCount <= 0) {
                    $this->cyclicFormulaCell = '';
                    return $this->raiseFormulaError('Cyclic Reference in Formula');
                } elseif ($this->cyclicFormulaCell === $wsCellReference) {
                    ++$this->cyclicFormulaCounter;
                    if ($this->cyclicFormulaCounter >= $this->cyclicFormulaCount) {
                        $this->cyclicFormulaCell = '';
                        return $cellValue;
                    }
                } elseif ($this->cyclicFormulaCell == '') {
                    if ($this->cyclicFormulaCounter >= $this->cyclicFormulaCount) {
                        return $cellValue;
                    }
                    $this->cyclicFormulaCell = $wsCellReference;
                }
            }
            //    Parse the formula onto the token stack and calculate the value
            $this->cyclicReferenceStack->push($wsCellReference);
            $cellValue = $this->processTokenStack($this->_parseFormula($formula, $pCell), $cellID, $pCell);
            $this->cyclicReferenceStack->pop();
            // Save to calculation cache
            if ($cellID !== null) {
                $this->saveValueToCache($wsCellReference, $cellValue);
            }
            //    Return the calculated value
            return $cellValue;
        }

        /**
         * Wrap string values in quotes
         * @param mixed $value
         * @return mixed
         */
        public static function wrapResult($value) {
            if (is_string($value)) {
                //    Error values cannot be "wrapped"
                if (preg_match('/^' . self::CALCULATION_REGEXP_ERROR . '$/i', $value, $match)) {
                    //    Return Excel errors "as is"
                    return $value;
                }
                //    Return strings wrapped in quotes
                return '"' . $value . '"';
                //    Convert numeric errors to NaN error
            } elseif ((is_float($value)) && ((is_nan($value)) || (is_infinite($value)))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return $value;
        }

        public function getValueFromCache($cellReference, &$cellValue) {
            // Is calculation cacheing enabled?
            // Is the value present in calculation cache?
            $this->_debugLog->writeDebugLog('Testing cache value for cell ', $cellReference);
            if (($this->calculationCacheEnabled) && (isset($this->calculationCache[$cellReference]))) {
                $this->_debugLog->writeDebugLog('Retrieving value for cell ', $cellReference, ' from cache');
                // Return the cached result
                $cellValue = $this->calculationCache[$cellReference];
                return true;
            }
            return false;
        }

        protected function raiseFormulaError($errorMessage) {
            $this->formulaError = $errorMessage;
            $this->cyclicReferenceStack->clear();
            if (!$this->suppressFormulaErrors) {
                throw new PHPExcel_Calculation_Exception($errorMessage);
            }
            trigger_error($errorMessage, E_USER_ERROR);
        }

        private function processTokenStack($tokens, $cellID = null, PHPExcel_Cell $pCell = null) {
            if ($tokens == false) {
                return false;
            }
            //    If we're using cell caching, then $pCell may well be flushed back to the cache (which detaches the parent cell collection),
            //        so we store the parent cell collection so that we can re-attach it when necessary
            $pCellWorksheet = ($pCell !== null) ? $pCell->getWorksheet() : null;
            $pCellParent    = ($pCell !== null) ? $pCell->getParent() : null;
            $stack          = new PHPExcel_Calculation_Token_Stack;
            //    Loop through each token in turn
            foreach ($tokens as $tokenData) {
                //            print_r($tokenData);
                //            echo '<br />';
                $token = $tokenData['value'];
                //            echo '<b>Token is '.$token.'</b><br />';
                // if the token is a binary operator, pop the top two values off the stack, do the operation, and push the result back on the stack
                if (isset(self::$binaryOperators[$token])) {
                    //                echo 'Token is a binary operator<br />';
                    //    We must have two operands, error if we don't
                    if (($operand2Data = $stack->pop()) === null) {
                        return $this->raiseFormulaError('Internal error - Operand value missing from stack');
                    }
                    if (($operand1Data = $stack->pop()) === null) {
                        return $this->raiseFormulaError('Internal error - Operand value missing from stack');
                    }
                    $operand1 = self::dataTestReference($operand1Data);
                    $operand2 = self::dataTestReference($operand2Data);
                    //    Log what we're doing
                    if ($token == ':') {
                        $this->_debugLog->writeDebugLog('Evaluating Range ', $this->showValue($operand1Data['reference']), ' ', $token, ' ', $this->showValue($operand2Data['reference']));
                    } else {
                        $this->_debugLog->writeDebugLog('Evaluating ', $this->showValue($operand1), ' ', $token, ' ', $this->showValue($operand2));
                    }
                    //    Process the operation in the appropriate manner
                    switch ($token) {
                        //    Comparison (Boolean) Operators
                        case '>':            //    Greater than
                        case '<':            //    Less than
                        case '>=':            //    Greater than or Equal to
                        case '<=':            //    Less than or Equal to
                        case '=':            //    Equality
                        case '<>':            //    Inequality
                            $this->executeBinaryComparisonOperation($cellID, $operand1, $operand2, $token, $stack);
                            break;
                        //    Binary Operators
                        case ':':            //    Range
                            $sheet1 = $sheet2 = '';
                            if (strpos($operand1Data['reference'], '!') !== false) {
                                list($sheet1, $operand1Data['reference']) = explode('!', $operand1Data['reference']);
                            } else {
                                $sheet1 = ($pCellParent !== null) ? $pCellWorksheet->getTitle() : '';
                            }
                            if (strpos($operand2Data['reference'], '!') !== false) {
                                list($sheet2, $operand2Data['reference']) = explode('!', $operand2Data['reference']);
                            } else {
                                $sheet2 = $sheet1;
                            }
                            if ($sheet1 == $sheet2) {
                                if ($operand1Data['reference'] === null) {
                                    if ((trim($operand1Data['value']) != '') && (is_numeric($operand1Data['value']))) {
                                        $operand1Data['reference'] = $pCell->getColumn() . $operand1Data['value'];
                                    } elseif (trim($operand1Data['reference']) == '') {
                                        $operand1Data['reference'] = $pCell->getCoordinate();
                                    } else {
                                        $operand1Data['reference'] = $operand1Data['value'] . $pCell->getRow();
                                    }
                                }
                                if ($operand2Data['reference'] === null) {
                                    if ((trim($operand2Data['value']) != '') && (is_numeric($operand2Data['value']))) {
                                        $operand2Data['reference'] = $pCell->getColumn() . $operand2Data['value'];
                                    } elseif (trim($operand2Data['reference']) == '') {
                                        $operand2Data['reference'] = $pCell->getCoordinate();
                                    } else {
                                        $operand2Data['reference'] = $operand2Data['value'] . $pCell->getRow();
                                    }
                                }
                                $oData = array_merge(explode(':', $operand1Data['reference']), explode(':', $operand2Data['reference']));
                                $oCol  = $oRow = [];
                                foreach ($oData as $oDatum) {
                                    $oCR    = PHPExcel_Cell::coordinateFromString($oDatum);
                                    $oCol[] = PHPExcel_Cell::columnIndexFromString($oCR[0]) - 1;
                                    $oRow[] = $oCR[1];
                                }
                                $cellRef = PHPExcel_Cell::stringFromColumnIndex(min($oCol)) . min($oRow) . ':' . PHPExcel_Cell::stringFromColumnIndex(max($oCol)) . max($oRow);
                                if ($pCellParent !== null) {
                                    $cellValue = $this->extractCellRange($cellRef, $this->workbook->getSheetByName($sheet1), false);
                                } else {
                                    return $this->raiseFormulaError('Unable to access Cell Reference');
                                }
                                $stack->push('Cell Reference', $cellValue, $cellRef);
                            } else {
                                $stack->push('Error', PHPExcel_Calculation_Functions::REF(), null);
                            }
                            break;
                        case '+':            //    Addition
                            $this->executeNumericBinaryOperation($cellID, $operand1, $operand2, $token, 'plusEquals', $stack);
                            break;
                        case '-':            //    Subtraction
                            $this->executeNumericBinaryOperation($cellID, $operand1, $operand2, $token, 'minusEquals', $stack);
                            break;
                        case '*':            //    Multiplication
                            $this->executeNumericBinaryOperation($cellID, $operand1, $operand2, $token, 'arrayTimesEquals', $stack);
                            break;
                        case '/':            //    Division
                            $this->executeNumericBinaryOperation($cellID, $operand1, $operand2, $token, 'arrayRightDivide', $stack);
                            break;
                        case '^':            //    Exponential
                            $this->executeNumericBinaryOperation($cellID, $operand1, $operand2, $token, 'power', $stack);
                            break;
                        case '&':            //    Concatenation
                            //    If either of the operands is a matrix, we need to treat them both as matrices
                            //        (converting the other operand to a matrix if need be); then perform the required
                            //        matrix operation
                            if (is_bool($operand1)) {
                                $operand1 = ($operand1) ? self::$localeBoolean['TRUE'] : self::$localeBoolean['FALSE'];
                            }
                            if (is_bool($operand2)) {
                                $operand2 = ($operand2) ? self::$localeBoolean['TRUE'] : self::$localeBoolean['FALSE'];
                            }
                            if ((is_array($operand1)) || (is_array($operand2))) {
                                //    Ensure that both operands are arrays/matrices
                                self::checkMatrixOperands($operand1, $operand2, 2);
                                try {
                                    //    Convert operand 1 from a PHP array to a matrix
                                    $matrix = new PHPExcel_Shared_JAMA_Matrix($operand1);
                                    //    Perform the required operation against the operand 1 matrix, passing in operand 2
                                    $matrixResult = $matrix->concat($operand2);
                                    $result       = $matrixResult->getArray();
                                } catch (PHPExcel_Exception $ex) {
                                    $this->_debugLog->writeDebugLog('JAMA Matrix Exception: ', $ex->getMessage());
                                    $result = '#VALUE!';
                                }
                            } else {
                                $result = '"' . str_replace('""', '"', self::unwrapResult($operand1, '"') . self::unwrapResult($operand2, '"')) . '"';
                            }
                            $this->_debugLog->writeDebugLog('Evaluation Result is ', $this->showTypeDetails($result));
                            $stack->push('Value', $result);
                            break;
                        case '|':            //    Intersect
                            $rowIntersect  = array_intersect_key($operand1, $operand2);
                            $cellIntersect = $oCol = $oRow = [];
                            foreach (array_keys($rowIntersect) as $row) {
                                $oRow[] = $row;
                                foreach ($rowIntersect[$row] as $col => $data) {
                                    $oCol[]              = PHPExcel_Cell::columnIndexFromString($col) - 1;
                                    $cellIntersect[$row] = array_intersect_key($operand1[$row], $operand2[$row]);
                                }
                            }
                            $cellRef = PHPExcel_Cell::stringFromColumnIndex(min($oCol)) . min($oRow) . ':' . PHPExcel_Cell::stringFromColumnIndex(max($oCol)) . max($oRow);
                            $this->_debugLog->writeDebugLog('Evaluation Result is ', $this->showTypeDetails($cellIntersect));
                            $stack->push('Value', $cellIntersect, $cellRef);
                            break;
                    }
                    // if the token is a unary operator, pop one value off the stack, do the operation, and push it back on
                } elseif (($token === '~') || ($token === '%')) {
                    //                echo 'Token is a unary operator<br />';
                    if (($arg = $stack->pop()) === null) {
                        return $this->raiseFormulaError('Internal error - Operand value missing from stack');
                    }
                    $arg = $arg['value'];
                    if ($token === '~') {
                        //                    echo 'Token is a negation operator<br />';
                        $this->_debugLog->writeDebugLog('Evaluating Negation of ', $this->showValue($arg));
                        $multiplier = -1;
                    } else {
                        //                    echo 'Token is a percentile operator<br />';
                        $this->_debugLog->writeDebugLog('Evaluating Percentile of ', $this->showValue($arg));
                        $multiplier = 0.01;
                    }
                    if (is_array($arg)) {
                        self::checkMatrixOperands($arg, $multiplier, 2);
                        try {
                            $matrix1      = new PHPExcel_Shared_JAMA_Matrix($arg);
                            $matrixResult = $matrix1->arrayTimesEquals($multiplier);
                            $result       = $matrixResult->getArray();
                        } catch (PHPExcel_Exception $ex) {
                            $this->_debugLog->writeDebugLog('JAMA Matrix Exception: ', $ex->getMessage());
                            $result = '#VALUE!';
                        }
                        $this->_debugLog->writeDebugLog('Evaluation Result is ', $this->showTypeDetails($result));
                        $stack->push('Value', $result);
                    } else {
                        $this->executeNumericBinaryOperation($cellID, $multiplier, $arg, '*', 'arrayTimesEquals', $stack);
                    }
                } elseif (preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '$/i', $token, $matches)) {
                    $cellRef = null;
                    //                echo 'Element '.$token.' is a Cell reference<br />';
                    if (isset($matches[8])) {
                        //                    echo 'Reference is a Range of cells<br />';
                        if ($pCell === null) {
                            //                        We can't access the range, so return a REF error
                            $cellValue = PHPExcel_Calculation_Functions::REF();
                        } else {
                            $cellRef = $matches[6] . $matches[7] . ':' . $matches[9] . $matches[10];
                            if ($matches[2] > '') {
                                $matches[2] = trim($matches[2], "\"'");
                                if ((strpos($matches[2], '[') !== false) || (strpos($matches[2], ']') !== false)) {
                                    //    It's a Reference to an external workbook (not currently supported)
                                    return $this->raiseFormulaError('Unable to access External Workbook');
                                }
                                $matches[2] = trim($matches[2], "\"'");
                                //                            echo '$cellRef='.$cellRef.' in worksheet '.$matches[2].'<br />';
                                $this->_debugLog->writeDebugLog('Evaluating Cell Range ', $cellRef, ' in worksheet ', $matches[2]);
                                if ($pCellParent !== null) {
                                    $cellValue = $this->extractCellRange($cellRef, $this->workbook->getSheetByName($matches[2]), false);
                                } else {
                                    return $this->raiseFormulaError('Unable to access Cell Reference');
                                }
                                $this->_debugLog->writeDebugLog('Evaluation Result for cells ', $cellRef, ' in worksheet ', $matches[2], ' is ', $this->showTypeDetails($cellValue));
                                //                            $cellRef = $matches[2].'!'.$cellRef;
                            } else {
                                //                            echo '$cellRef='.$cellRef.' in current worksheet<br />';
                                $this->_debugLog->writeDebugLog('Evaluating Cell Range ', $cellRef, ' in current worksheet');
                                if ($pCellParent !== null) {
                                    $cellValue = $this->extractCellRange($cellRef, $pCellWorksheet, false);
                                } else {
                                    return $this->raiseFormulaError('Unable to access Cell Reference');
                                }
                                $this->_debugLog->writeDebugLog('Evaluation Result for cells ', $cellRef, ' is ', $this->showTypeDetails($cellValue));
                            }
                        }
                    } else {
                        //                    echo 'Reference is a single Cell<br />';
                        if ($pCell === null) {
                            //                        We can't access the cell, so return a REF error
                            $cellValue = PHPExcel_Calculation_Functions::REF();
                        } else {
                            $cellRef = $matches[6] . $matches[7];
                            if ($matches[2] > '') {
                                $matches[2] = trim($matches[2], "\"'");
                                if ((strpos($matches[2], '[') !== false) || (strpos($matches[2], ']') !== false)) {
                                    //    It's a Reference to an external workbook (not currently supported)
                                    return $this->raiseFormulaError('Unable to access External Workbook');
                                }
                                //                            echo '$cellRef='.$cellRef.' in worksheet '.$matches[2].'<br />';
                                $this->_debugLog->writeDebugLog('Evaluating Cell ', $cellRef, ' in worksheet ', $matches[2]);
                                if ($pCellParent !== null) {
                                    $cellSheet = $this->workbook->getSheetByName($matches[2]);
                                    if ($cellSheet && $cellSheet->cellExists($cellRef)) {
                                        $cellValue = $this->extractCellRange($cellRef, $this->workbook->getSheetByName($matches[2]), false);
                                        $pCell->attach($pCellParent);
                                    } else {
                                        $cellValue = null;
                                    }
                                } else {
                                    return $this->raiseFormulaError('Unable to access Cell Reference');
                                }
                                $this->_debugLog->writeDebugLog('Evaluation Result for cell ', $cellRef, ' in worksheet ', $matches[2], ' is ', $this->showTypeDetails($cellValue));
                                //                            $cellRef = $matches[2].'!'.$cellRef;
                            } else {
                                //                            echo '$cellRef='.$cellRef.' in current worksheet<br />';
                                $this->_debugLog->writeDebugLog('Evaluating Cell ', $cellRef, ' in current worksheet');
                                if ($pCellParent->isDataSet($cellRef)) {
                                    $cellValue = $this->extractCellRange($cellRef, $pCellWorksheet, false);
                                    $pCell->attach($pCellParent);
                                } else {
                                    $cellValue = null;
                                }
                                $this->_debugLog->writeDebugLog('Evaluation Result for cell ', $cellRef, ' is ', $this->showTypeDetails($cellValue));
                            }
                        }
                    }
                    $stack->push('Value', $cellValue, $cellRef);
                    // if the token is a function, pop arguments off the stack, hand them to the function, and push the result back on
                } elseif (preg_match('/^' . self::CALCULATION_REGEXP_FUNCTION . '$/i', $token, $matches)) {
                    //                echo 'Token is a function<br />';
                    $functionName = $matches[1];
                    $argCount     = $stack->pop();
                    $argCount     = $argCount['value'];
                    if ($functionName != 'MKMATRIX') {
                        $this->_debugLog->writeDebugLog('Evaluating Function ', self::localeFunc($functionName), '() with ', (($argCount == 0) ? 'no' : $argCount), ' argument', (($argCount == 1) ? '' : 's'));
                    }
                    if ((isset(self::$PHPExcelFunctions[$functionName])) || (isset(self::$controlFunctions[$functionName]))) {    // function
                        if (isset(self::$PHPExcelFunctions[$functionName])) {
                            $functionCall      = self::$PHPExcelFunctions[$functionName]['functionCall'];
                            $passByReference   = isset(self::$PHPExcelFunctions[$functionName]['passByReference']);
                            $passCellReference = isset(self::$PHPExcelFunctions[$functionName]['passCellReference']);
                        } elseif (isset(self::$controlFunctions[$functionName])) {
                            $functionCall      = self::$controlFunctions[$functionName]['functionCall'];
                            $passByReference   = isset(self::$controlFunctions[$functionName]['passByReference']);
                            $passCellReference = isset(self::$controlFunctions[$functionName]['passCellReference']);
                        }
                        // get the arguments for this function
                        //                    echo 'Function '.$functionName.' expects '.$argCount.' arguments<br />';
                        $args = $argArrayVals = [];
                        for ($i = 0; $i < $argCount; ++$i) {
                            $arg = $stack->pop();
                            $a   = $argCount - $i - 1;
                            if (($passByReference) && (isset(self::$PHPExcelFunctions[$functionName]['passByReference'][$a])) && (self::$PHPExcelFunctions[$functionName]['passByReference'][$a])) {
                                if ($arg['reference'] === null) {
                                    $args[] = $cellID;
                                    if ($functionName != 'MKMATRIX') {
                                        $argArrayVals[] = $this->showValue($cellID);
                                    }
                                } else {
                                    $args[] = $arg['reference'];
                                    if ($functionName != 'MKMATRIX') {
                                        $argArrayVals[] = $this->showValue($arg['reference']);
                                    }
                                }
                            } else {
                                $args[] = self::unwrapResult($arg['value']);
                                if ($functionName != 'MKMATRIX') {
                                    $argArrayVals[] = $this->showValue($arg['value']);
                                }
                            }
                        }
                        //    Reverse the order of the arguments
                        krsort($args);
                        if (($passByReference) && ($argCount == 0)) {
                            $args[]         = $cellID;
                            $argArrayVals[] = $this->showValue($cellID);
                        }
                        //                    echo 'Arguments are: ';
                        //                    print_r($args);
                        //                    echo '<br />';
                        if ($functionName != 'MKMATRIX') {
                            if ($this->_debugLog->getWriteDebugLog()) {
                                krsort($argArrayVals);
                                $this->_debugLog->writeDebugLog('Evaluating ', self::localeFunc($functionName), '( ', implode(self::$localeArgumentSeparator . ' ', PHPExcel_Calculation_Functions::flattenArray($argArrayVals)), ' )');
                            }
                        }
                        //    Process each argument in turn, building the return value as an array
                        //                    if (($argCount == 1) && (is_array($args[1])) && ($functionName != 'MKMATRIX')) {
                        //                        $operand1 = $args[1];
                        //                        $this->_debugLog->writeDebugLog('Argument is a matrix: ', $this->showValue($operand1));
                        //                        $result = array();
                        //                        $row = 0;
                        //                        foreach($operand1 as $args) {
                        //                            if (is_array($args)) {
                        //                                foreach($args as $arg) {
                        //                                    $this->_debugLog->writeDebugLog('Evaluating ', self::localeFunc($functionName), '( ', $this->showValue($arg), ' )');
                        //                                    $r = call_user_func_array($functionCall, $arg);
                        //                                    $this->_debugLog->writeDebugLog('Evaluation Result for ', self::localeFunc($functionName), '() function call is ', $this->showTypeDetails($r));
                        //                                    $result[$row][] = $r;
                        //                                }
                        //                                ++$row;
                        //                            } else {
                        //                                $this->_debugLog->writeDebugLog('Evaluating ', self::localeFunc($functionName), '( ', $this->showValue($args), ' )');
                        //                                $r = call_user_func_array($functionCall, $args);
                        //                                $this->_debugLog->writeDebugLog('Evaluation Result for ', self::localeFunc($functionName), '() function call is ', $this->showTypeDetails($r));
                        //                                $result[] = $r;
                        //                            }
                        //                        }
                        //                    } else {
                        //    Process the argument with the appropriate function call
                        if ($passCellReference) {
                            $args[] = $pCell;
                        }
                        if (strpos($functionCall, '::') !== false) {
                            $result = call_user_func_array(explode('::', $functionCall), $args);
                        } else {
                            foreach ($args as &$arg) {
                                $arg = PHPExcel_Calculation_Functions::flattenSingleValue($arg);
                            }
                            unset($arg);
                            $result = call_user_func_array($functionCall, $args);
                        }
                        if ($functionName != 'MKMATRIX') {
                            $this->_debugLog->writeDebugLog('Evaluation Result for ', self::localeFunc($functionName), '() function call is ', $this->showTypeDetails($result));
                        }
                        $stack->push('Value', self::wrapResult($result));
                    }
                } else {
                    // if the token is a number, boolean, string or an Excel error, push it onto the stack
                    if (isset(self::$excelConstants[strtoupper($token)])) {
                        $excelConstant = strtoupper($token);
                        //                    echo 'Token is a PHPExcel constant: '.$excelConstant.'<br />';
                        $stack->push('Constant Value', self::$excelConstants[$excelConstant]);
                        $this->_debugLog->writeDebugLog('Evaluating Constant ', $excelConstant, ' as ', $this->showTypeDetails(self::$excelConstants[$excelConstant]));
                    } elseif ((is_numeric($token)) || ($token === null) || (is_bool($token)) || ($token == '') || ($token{0} == '"') || ($token{0} == '#')) {
                        //                    echo 'Token is a number, boolean, string, null or an Excel error<br />';
                        $stack->push('Value', $token);
                        // if the token is a named range, push the named range name onto the stack
                    } elseif (preg_match('/^' . self::CALCULATION_REGEXP_NAMEDRANGE . '$/i', $token, $matches)) {
                        //                    echo 'Token is a named range<br />';
                        $namedRange = $matches[6];
                        //                    echo 'Named Range is '.$namedRange.'<br />';
                        $this->_debugLog->writeDebugLog('Evaluating Named Range ', $namedRange);
                        $cellValue = $this->extractNamedRange($namedRange, ((null !== $pCell) ? $pCellWorksheet : null), false);
                        $pCell->attach($pCellParent);
                        $this->_debugLog->writeDebugLog('Evaluation Result for named range ', $namedRange, ' is ', $this->showTypeDetails($cellValue));
                        $stack->push('Named Range', $cellValue, $namedRange);
                    } else {
                        return $this->raiseFormulaError("undefined variable '$token'");
                    }
                }
            }
            // when we're out of tokens, the stack should have a single element, the final result
            if ($stack->count() != 1) {
                return $this->raiseFormulaError("internal error");
            }
            $output = $stack->pop();
            $output = $output['value'];
            //        if ((is_array($output)) && (self::$returnArrayAsType != self::RETURN_ARRAY_AS_ARRAY)) {
            //            return array_shift(PHPExcel_Calculation_Functions::flattenArray($output));
            //        }
            return $output;
        }

        private static function dataTestReference(&$operandData) {
            $operand = $operandData['value'];
            if (($operandData['reference'] === null) && (is_array($operand))) {
                $rKeys  = array_keys($operand);
                $rowKey = array_shift($rKeys);
                $cKeys  = array_keys(array_keys($operand[$rowKey]));
                $colKey = array_shift($cKeys);
                if (ctype_upper($colKey)) {
                    $operandData['reference'] = $colKey . $rowKey;
                }
            }
            return $operand;
        }

        /**
         * Format details of an operand for display in the log (based on operand type)
         * @param    mixed $value First matrix operand
         * @return    mixed
         */
        private function showValue($value) {
            if ($this->_debugLog->getWriteDebugLog()) {
                $testArray = PHPExcel_Calculation_Functions::flattenArray($value);
                if (count($testArray) == 1) {
                    $value = array_pop($testArray);
                }
                if (is_array($value)) {
                    $returnMatrix = [];
                    $pad          = $rpad = ', ';
                    foreach ($value as $row) {
                        if (is_array($row)) {
                            $returnMatrix[] = implode($pad, array_map([
                                                                          $this,
                                                                          'showValue'
                                                                      ], $row
                            )
                            );
                            $rpad           = '; ';
                        } else {
                            $returnMatrix[] = $this->showValue($row);
                        }
                    }
                    return '{ ' . implode($rpad, $returnMatrix) . ' }';
                } elseif (is_string($value) && (trim($value, '"') == $value)) {
                    return '"' . $value . '"';
                } elseif (is_bool($value)) {
                    return ($value) ? self::$localeBoolean['TRUE'] : self::$localeBoolean['FALSE'];
                }
            }
            return PHPExcel_Calculation_Functions::flattenSingleValue($value);
        }

        private function executeBinaryComparisonOperation($cellID, $operand1, $operand2, $operation, &$stack, $recursingArrays = false) {
            //    If we're dealing with matrix operations, we want a matrix result
            if ((is_array($operand1)) || (is_array($operand2))) {
                $result = [];
                if ((is_array($operand1)) && (!is_array($operand2))) {
                    foreach ($operand1 as $x => $operandData) {
                        $this->_debugLog->writeDebugLog('Evaluating Comparison ', $this->showValue($operandData), ' ', $operation, ' ', $this->showValue($operand2));
                        $this->executeBinaryComparisonOperation($cellID, $operandData, $operand2, $operation, $stack);
                        $r          = $stack->pop();
                        $result[$x] = $r['value'];
                    }
                } elseif ((!is_array($operand1)) && (is_array($operand2))) {
                    foreach ($operand2 as $x => $operandData) {
                        $this->_debugLog->writeDebugLog('Evaluating Comparison ', $this->showValue($operand1), ' ', $operation, ' ', $this->showValue($operandData));
                        $this->executeBinaryComparisonOperation($cellID, $operand1, $operandData, $operation, $stack);
                        $r          = $stack->pop();
                        $result[$x] = $r['value'];
                    }
                } else {
                    if (!$recursingArrays) {
                        self::checkMatrixOperands($operand1, $operand2, 2);
                    }
                    foreach ($operand1 as $x => $operandData) {
                        $this->_debugLog->writeDebugLog('Evaluating Comparison ', $this->showValue($operandData), ' ', $operation, ' ', $this->showValue($operand2[$x]));
                        $this->executeBinaryComparisonOperation($cellID, $operandData, $operand2[$x], $operation, $stack, true);
                        $r          = $stack->pop();
                        $result[$x] = $r['value'];
                    }
                }
                //    Log the result details
                $this->_debugLog->writeDebugLog('Comparison Evaluation Result is ', $this->showTypeDetails($result));
                //    And push the result onto the stack
                $stack->push('Array', $result);
                return true;
            }
            //    Simple validate the two operands if they are string values
            if (is_string($operand1) && $operand1 > '' && $operand1{0} == '"') {
                $operand1 = self::unwrapResult($operand1);
            }
            if (is_string($operand2) && $operand2 > '' && $operand2{0} == '"') {
                $operand2 = self::unwrapResult($operand2);
            }
            // Use case insensitive comparaison if not OpenOffice mode
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() != PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                if (is_string($operand1)) {
                    $operand1 = strtoupper($operand1);
                }
                if (is_string($operand2)) {
                    $operand2 = strtoupper($operand2);
                }
            }
            $useLowercaseFirstComparison = is_string($operand1) && is_string($operand2) && PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE;
            //    execute the necessary operation
            switch ($operation) {
                //    Greater than
                case '>':
                    if ($useLowercaseFirstComparison) {
                        $result = $this->strcmpLowercaseFirst($operand1, $operand2) > 0;
                    } else {
                        $result = ($operand1 > $operand2);
                    }
                    break;
                //    Less than
                case '<':
                    if ($useLowercaseFirstComparison) {
                        $result = $this->strcmpLowercaseFirst($operand1, $operand2) < 0;
                    } else {
                        $result = ($operand1 < $operand2);
                    }
                    break;
                //    Equality
                case '=':
                    if (is_numeric($operand1) && is_numeric($operand2)) {
                        $result = (abs($operand1 - $operand2) < $this->delta);
                    } else {
                        $result = strcmp($operand1, $operand2) == 0;
                    }
                    break;
                //    Greater than or equal
                case '>=':
                    if (is_numeric($operand1) && is_numeric($operand2)) {
                        $result = ((abs($operand1 - $operand2) < $this->delta) || ($operand1 > $operand2));
                    } elseif ($useLowercaseFirstComparison) {
                        $result = $this->strcmpLowercaseFirst($operand1, $operand2) >= 0;
                    } else {
                        $result = strcmp($operand1, $operand2) >= 0;
                    }
                    break;
                //    Less than or equal
                case '<=':
                    if (is_numeric($operand1) && is_numeric($operand2)) {
                        $result = ((abs($operand1 - $operand2) < $this->delta) || ($operand1 < $operand2));
                    } elseif ($useLowercaseFirstComparison) {
                        $result = $this->strcmpLowercaseFirst($operand1, $operand2) <= 0;
                    } else {
                        $result = strcmp($operand1, $operand2) <= 0;
                    }
                    break;
                //    Inequality
                case '<>':
                    if (is_numeric($operand1) && is_numeric($operand2)) {
                        $result = (abs($operand1 - $operand2) > 1E-14);
                    } else {
                        $result = strcmp($operand1, $operand2) != 0;
                    }
                    break;
            }
            //    Log the result details
            $this->_debugLog->writeDebugLog('Evaluation Result is ', $this->showTypeDetails($result));
            //    And push the result onto the stack
            $stack->push('Value', $result);
            return true;
        }

        /**
         * Ensure that paired matrix operands are both matrices and of the same size
         * @param    mixed   &$operand1               First matrix operand
         * @param    mixed   &$operand2               Second matrix operand
         * @param    integer $resize                  Flag indicating whether the matrices should be resized to match
         *                                            and (if so), whether the smaller dimension should grow or the
         *                                            larger should shrink.
         *                                            0 = no resize
         *                                            1 = shrink to fit
         *                                            2 = extend to fit
         */
        private static function checkMatrixOperands(&$operand1, &$operand2, $resize = 1) {
            //    Examine each of the two operands, and turn them into an array if they aren't one already
            //    Note that this function should only be called if one or both of the operand is already an array
            if (!is_array($operand1)) {
                list($matrixRows, $matrixColumns) = self::getMatrixDimensions($operand2);
                $operand1 = array_fill(0, $matrixRows, array_fill(0, $matrixColumns, $operand1));
                $resize   = 0;
            } elseif (!is_array($operand2)) {
                list($matrixRows, $matrixColumns) = self::getMatrixDimensions($operand1);
                $operand2 = array_fill(0, $matrixRows, array_fill(0, $matrixColumns, $operand2));
                $resize   = 0;
            }
            list($matrix1Rows, $matrix1Columns) = self::getMatrixDimensions($operand1);
            list($matrix2Rows, $matrix2Columns) = self::getMatrixDimensions($operand2);
            if (($matrix1Rows == $matrix2Columns) && ($matrix2Rows == $matrix1Columns)) {
                $resize = 1;
            }
            if ($resize == 2) {
                //    Given two matrices of (potentially) unequal size, convert the smaller in each dimension to match the larger
                self::resizeMatricesExtend($operand1, $operand2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns);
            } elseif ($resize == 1) {
                //    Given two matrices of (potentially) unequal size, convert the larger in each dimension to match the smaller
                self::resizeMatricesShrink($operand1, $operand2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns);
            }
            return [
                $matrix1Rows,
                $matrix1Columns,
                $matrix2Rows,
                $matrix2Columns
            ];
        }

        /**
         * Read the dimensions of a matrix, and re-index it with straight numeric keys starting from row 0, column 0
         * @param    mixed &$matrix matrix operand
         * @return    array        An array comprising the number of rows, and number of columns
         */
        private static function getMatrixDimensions(&$matrix) {
            $matrixRows    = count($matrix);
            $matrixColumns = 0;
            foreach ($matrix as $rowKey => $rowValue) {
                $matrixColumns = max(count($rowValue), $matrixColumns);
                if (!is_array($rowValue)) {
                    $matrix[$rowKey] = [$rowValue];
                } else {
                    $matrix[$rowKey] = array_values($rowValue);
                }
            }
            $matrix = array_values($matrix);
            return [
                $matrixRows,
                $matrixColumns
            ];
        }

        /**
         * Ensure that paired matrix operands are both matrices of the same size
         * @param    mixed   &$matrix1       First matrix operand
         * @param    mixed   &$matrix2       Second matrix operand
         * @param    integer $matrix1Rows    Row size of first matrix operand
         * @param    integer $matrix1Columns Column size of first matrix operand
         * @param    integer $matrix2Rows    Row size of second matrix operand
         * @param    integer $matrix2Columns Column size of second matrix operand
         */
        private static function resizeMatricesExtend(&$matrix1, &$matrix2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns) {
            if (($matrix2Columns < $matrix1Columns) || ($matrix2Rows < $matrix1Rows)) {
                if ($matrix2Columns < $matrix1Columns) {
                    for ($i = 0; $i < $matrix2Rows; ++$i) {
                        $x = $matrix2[$i][$matrix2Columns - 1];
                        for ($j = $matrix2Columns; $j < $matrix1Columns; ++$j) {
                            $matrix2[$i][$j] = $x;
                        }
                    }
                }
                if ($matrix2Rows < $matrix1Rows) {
                    $x = $matrix2[$matrix2Rows - 1];
                    for ($i = 0; $i < $matrix1Rows; ++$i) {
                        $matrix2[$i] = $x;
                    }
                }
            }
            if (($matrix1Columns < $matrix2Columns) || ($matrix1Rows < $matrix2Rows)) {
                if ($matrix1Columns < $matrix2Columns) {
                    for ($i = 0; $i < $matrix1Rows; ++$i) {
                        $x = $matrix1[$i][$matrix1Columns - 1];
                        for ($j = $matrix1Columns; $j < $matrix2Columns; ++$j) {
                            $matrix1[$i][$j] = $x;
                        }
                    }
                }
                if ($matrix1Rows < $matrix2Rows) {
                    $x = $matrix1[$matrix1Rows - 1];
                    for ($i = 0; $i < $matrix2Rows; ++$i) {
                        $matrix1[$i] = $x;
                    }
                }
            }
        }

        /**
         * Ensure that paired matrix operands are both matrices of the same size
         * @param    mixed   &$matrix1       First matrix operand
         * @param    mixed   &$matrix2       Second matrix operand
         * @param    integer $matrix1Rows    Row size of first matrix operand
         * @param    integer $matrix1Columns Column size of first matrix operand
         * @param    integer $matrix2Rows    Row size of second matrix operand
         * @param    integer $matrix2Columns Column size of second matrix operand
         */
        private static function resizeMatricesShrink(&$matrix1, &$matrix2, $matrix1Rows, $matrix1Columns, $matrix2Rows, $matrix2Columns) {
            if (($matrix2Columns < $matrix1Columns) || ($matrix2Rows < $matrix1Rows)) {
                if ($matrix2Rows < $matrix1Rows) {
                    for ($i = $matrix2Rows; $i < $matrix1Rows; ++$i) {
                        unset($matrix1[$i]);
                    }
                }
                if ($matrix2Columns < $matrix1Columns) {
                    for ($i = 0; $i < $matrix1Rows; ++$i) {
                        for ($j = $matrix2Columns; $j < $matrix1Columns; ++$j) {
                            unset($matrix1[$i][$j]);
                        }
                    }
                }
            }
            if (($matrix1Columns < $matrix2Columns) || ($matrix1Rows < $matrix2Rows)) {
                if ($matrix1Rows < $matrix2Rows) {
                    for ($i = $matrix1Rows; $i < $matrix2Rows; ++$i) {
                        unset($matrix2[$i]);
                    }
                }
                if ($matrix1Columns < $matrix2Columns) {
                    for ($i = 0; $i < $matrix2Rows; ++$i) {
                        for ($j = $matrix1Columns; $j < $matrix2Columns; ++$j) {
                            unset($matrix2[$i][$j]);
                        }
                    }
                }
            }
        }

        /**
         * Format type and details of an operand for display in the log (based on operand type)
         * @param    mixed $value First matrix operand
         * @return    mixed
         */
        private function showTypeDetails($value) {
            if ($this->_debugLog->getWriteDebugLog()) {
                $testArray = PHPExcel_Calculation_Functions::flattenArray($value);
                if (count($testArray) == 1) {
                    $value = array_pop($testArray);
                }
                if ($value === null) {
                    return 'a NULL value';
                } elseif (is_float($value)) {
                    $typeString = 'a floating point number';
                } elseif (is_int($value)) {
                    $typeString = 'an integer number';
                } elseif (is_bool($value)) {
                    $typeString = 'a boolean';
                } elseif (is_array($value)) {
                    $typeString = 'a matrix';
                } else {
                    if ($value == '') {
                        return 'an empty string';
                    } elseif ($value{0} == '#') {
                        return 'a ' . $value . ' error';
                    } else {
                        $typeString = 'a string';
                    }
                }
                return $typeString . ' with a value of ' . $this->showValue($value);
            }
        }


        //    Binary Operators
        //    These operators always work on two values
        //    Array key is the operator, the value indicates whether this is a left or right associative operator
        /**
         * Compare two strings in the same way as strcmp() except that lowercase come before uppercase letters
         * @param    string $str1 First string value for the comparison
         * @param    string $str2 Second string value for the comparison
         * @return   integer
         */
        private function strcmpLowercaseFirst($str1, $str2) {
            $inversedStr1 = PHPExcel_Shared_String::StrCaseReverse($str1);
            $inversedStr2 = PHPExcel_Shared_String::StrCaseReverse($str2);
            return strcmp($inversedStr1, $inversedStr2);
        }

        //    Comparison (Boolean) Operators
        //    These operators work on two values, but always return a boolean result
        /**
         * Extract range values
         * @param    string             &$pRange  String based range representation
         * @param    PHPExcel_Worksheet $pSheet   Worksheet
         * @param    boolean            $resetLog Flag indicating whether calculation log should be reset or not
         * @return  mixed                Array of values in range if range contains more than one element. Otherwise, a single value is returned.
         * @throws    PHPExcel_Calculation_Exception
         */
        public function extractCellRange(&$pRange = 'A1', PHPExcel_Worksheet $pSheet = null, $resetLog = true) {
            // Return value
            $returnValue = [];
            //        echo 'extractCellRange('.$pRange.')', PHP_EOL;
            if ($pSheet !== null) {
                $pSheetName = $pSheet->getTitle();
                //            echo 'Passed sheet name is '.$pSheetName.PHP_EOL;
                //            echo 'Range reference is '.$pRange.PHP_EOL;
                if (strpos($pRange, '!') !== false) {
                    //                echo '$pRange reference includes sheet reference', PHP_EOL;
                    list($pSheetName, $pRange) = PHPExcel_Worksheet::extractSheetTitle($pRange, true);
                    //                echo 'New sheet name is '.$pSheetName, PHP_EOL;
                    //                echo 'Adjusted Range reference is '.$pRange, PHP_EOL;
                    $pSheet = $this->workbook->getSheetByName($pSheetName);
                }
                // Extract range
                $aReferences = PHPExcel_Cell::extractAllCellReferencesInRange($pRange);
                $pRange      = $pSheetName . '!' . $pRange;
                if (!isset($aReferences[1])) {
                    //    Single cell in range
                    sscanf($aReferences[0], '%[A-Z]%d', $currentCol, $currentRow);
                    $cellValue = null;
                    if ($pSheet->cellExists($aReferences[0])) {
                        $returnValue[$currentRow][$currentCol] = $pSheet->getCell($aReferences[0])->getCalculatedValue($resetLog);
                    } else {
                        $returnValue[$currentRow][$currentCol] = null;
                    }
                } else {
                    // Extract cell data for all cells in the range
                    foreach ($aReferences as $reference) {
                        // Extract range
                        sscanf($reference, '%[A-Z]%d', $currentCol, $currentRow);
                        $cellValue = null;
                        if ($pSheet->cellExists($reference)) {
                            $returnValue[$currentRow][$currentCol] = $pSheet->getCell($reference)->getCalculatedValue($resetLog);
                        } else {
                            $returnValue[$currentRow][$currentCol] = null;
                        }
                    }
                }
            }
            return $returnValue;
        }

        //    Operator Precedence
        //    This list includes all valid operators, whether binary (including boolean) or unary (such as %)
        //    Array key is the operator, the value is its precedence
        private function executeNumericBinaryOperation($cellID, $operand1, $operand2, $operation, $matrixFunction, &$stack) {
            //    Validate the two operands
            if (!$this->validateBinaryOperand($cellID, $operand1, $stack)) {
                return false;
            }
            if (!$this->validateBinaryOperand($cellID, $operand2, $stack)) {
                return false;
            }
            //    If either of the operands is a matrix, we need to treat them both as matrices
            //        (converting the other operand to a matrix if need be); then perform the required
            //        matrix operation
            if ((is_array($operand1)) || (is_array($operand2))) {
                //    Ensure that both operands are arrays/matrices of the same size
                self::checkMatrixOperands($operand1, $operand2, 2);
                try {
                    //    Convert operand 1 from a PHP array to a matrix
                    $matrix = new PHPExcel_Shared_JAMA_Matrix($operand1);
                    //    Perform the required operation against the operand 1 matrix, passing in operand 2
                    $matrixResult = $matrix->$matrixFunction($operand2);
                    $result       = $matrixResult->getArray();
                } catch (PHPExcel_Exception $ex) {
                    $this->_debugLog->writeDebugLog('JAMA Matrix Exception: ', $ex->getMessage());
                    $result = '#VALUE!';
                }
            } else {
                if ((PHPExcel_Calculation_Functions::getCompatibilityMode() != PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) && ((is_string($operand1) && !is_numeric($operand1) && strlen($operand1) > 0) || (is_string($operand2) && !is_numeric($operand2) && strlen($operand2) > 0))) {
                    $result = PHPExcel_Calculation_Functions::VALUE();
                } else {
                    //    If we're dealing with non-matrix operations, execute the necessary operation
                    switch ($operation) {
                        //    Addition
                        case '+':
                            $result = $operand1 + $operand2;
                            break;
                        //    Subtraction
                        case '-':
                            $result = $operand1 - $operand2;
                            break;
                        //    Multiplication
                        case '*':
                            $result = $operand1 * $operand2;
                            break;
                        //    Division
                        case '/':
                            if ($operand2 == 0) {
                                //    Trap for Divide by Zero error
                                $stack->push('Value', '#DIV/0!');
                                $this->_debugLog->writeDebugLog('Evaluation Result is ', $this->showTypeDetails('#DIV/0!'));
                                return false;
                            } else {
                                $result = $operand1 / $operand2;
                            }
                            break;
                        //    Power
                        case '^':
                            $result = pow($operand1, $operand2);
                            break;
                    }
                }
            }
            //    Log the result details
            $this->_debugLog->writeDebugLog('Evaluation Result is ', $this->showTypeDetails($result));
            //    And push the result onto the stack
            $stack->push('Value', $result);
            return true;
        }

        // Convert infix to postfix notation
        private function validateBinaryOperand($cellID, &$operand, &$stack) {
            if (is_array($operand)) {
                if ((count($operand, COUNT_RECURSIVE) - count($operand)) == 1) {
                    do {
                        $operand = array_pop($operand);
                    } while (is_array($operand));
                }
            }
            //    Numbers, matrices and booleans can pass straight through, as they're already valid
            if (is_string($operand)) {
                //    We only need special validations for the operand if it is a string
                //    Start by stripping off the quotation marks we use to identify true excel string values internally
                if ($operand > '' && $operand{0} == '"') {
                    $operand = self::unwrapResult($operand);
                }
                //    If the string is a numeric value, we treat it as a numeric, so no further testing
                if (!is_numeric($operand)) {
                    //    If not a numeric, test to see if the value is an Excel error, and so can't be used in normal binary operations
                    if ($operand > '' && $operand{0} == '#') {
                        $stack->push('Value', $operand);
                        $this->_debugLog->writeDebugLog('Evaluation Result is ', $this->showTypeDetails($operand));
                        return false;
                    } elseif (!PHPExcel_Shared_String::convertToNumberIfFraction($operand)) {
                        //    If not a numeric or a fraction, then it's a text string, and so can't be used in mathematical binary operations
                        $stack->push('Value', '#VALUE!');
                        $this->_debugLog->writeDebugLog('Evaluation Result is a ', $this->showTypeDetails('#VALUE!'));
                        return false;
                    }
                }
            }
            //    return a true if the value of the operand is one that we can use in normal binary operations
            return true;
        }

        public static function localeFunc($function) {
            if (self::$localeLanguage !== 'en_us') {
                $functionName = trim($function, '(');
                if (isset(self::$localeFunctions[$functionName])) {
                    $brace    = ($functionName != $function);
                    $function = self::$localeFunctions[$functionName];
                    if ($brace) {
                        $function .= '(';
                    }
                }
            }
            return $function;
        }

        // evaluate postfix notation

        /**
         * Extract range values
         * @param    string             &$pRange  String based range representation
         * @param    PHPExcel_Worksheet $pSheet   Worksheet
         * @return  mixed                Array of values in range if range contains more than one element. Otherwise, a single value is returned.
         * @param    boolean            $resetLog Flag indicating whether calculation log should be reset or not
         * @throws    PHPExcel_Calculation_Exception
         */
        public function extractNamedRange(&$pRange = 'A1', PHPExcel_Worksheet $pSheet = null, $resetLog = true) {
            // Return value
            $returnValue = [];
            //        echo 'extractNamedRange('.$pRange.')<br />';
            if ($pSheet !== null) {
                $pSheetName = $pSheet->getTitle();
                //            echo 'Current sheet name is '.$pSheetName.'<br />';
                //            echo 'Range reference is '.$pRange.'<br />';
                if (strpos($pRange, '!') !== false) {
                    //                echo '$pRange reference includes sheet reference', PHP_EOL;
                    list($pSheetName, $pRange) = PHPExcel_Worksheet::extractSheetTitle($pRange, true);
                    //                echo 'New sheet name is '.$pSheetName, PHP_EOL;
                    //                echo 'Adjusted Range reference is '.$pRange, PHP_EOL;
                    $pSheet = $this->workbook->getSheetByName($pSheetName);
                }
                // Named range?
                $namedRange = PHPExcel_NamedRange::resolveRange($pRange, $pSheet);
                if ($namedRange !== null) {
                    $pSheet = $namedRange->getWorksheet();
                    //                echo 'Named Range '.$pRange.' (';
                    $pRange     = $namedRange->getRange();
                    $splitRange = PHPExcel_Cell::splitRange($pRange);
                    //    Convert row and column references
                    if (ctype_alpha($splitRange[0][0])) {
                        $pRange = $splitRange[0][0] . '1:' . $splitRange[0][1] . $namedRange->getWorksheet()->getHighestRow();
                    } elseif (ctype_digit($splitRange[0][0])) {
                        $pRange = 'A' . $splitRange[0][0] . ':' . $namedRange->getWorksheet()->getHighestColumn() . $splitRange[0][1];
                    }
                    //                echo $pRange.') is in sheet '.$namedRange->getWorksheet()->getTitle().'<br />';
                    //                if ($pSheet->getTitle() != $namedRange->getWorksheet()->getTitle()) {
                    //                    if (!$namedRange->getLocalOnly()) {
                    //                        $pSheet = $namedRange->getWorksheet();
                    //                    } else {
                    //                        return $returnValue;
                    //                    }
                    //                }
                } else {
                    return PHPExcel_Calculation_Functions::REF();
                }
                // Extract range
                $aReferences = PHPExcel_Cell::extractAllCellReferencesInRange($pRange);
                //            var_dump($aReferences);
                if (!isset($aReferences[1])) {
                    //    Single cell (or single column or row) in range
                    list($currentCol, $currentRow) = PHPExcel_Cell::coordinateFromString($aReferences[0]);
                    $cellValue = null;
                    if ($pSheet->cellExists($aReferences[0])) {
                        $returnValue[$currentRow][$currentCol] = $pSheet->getCell($aReferences[0])->getCalculatedValue($resetLog);
                    } else {
                        $returnValue[$currentRow][$currentCol] = null;
                    }
                } else {
                    // Extract cell data for all cells in the range
                    foreach ($aReferences as $reference) {
                        // Extract range
                        list($currentCol, $currentRow) = PHPExcel_Cell::coordinateFromString($reference);
                        //                    echo 'NAMED RANGE: $currentCol='.$currentCol.' $currentRow='.$currentRow.'<br />';
                        $cellValue = null;
                        if ($pSheet->cellExists($reference)) {
                            $returnValue[$currentRow][$currentCol] = $pSheet->getCell($reference)->getCalculatedValue($resetLog);
                        } else {
                            $returnValue[$currentRow][$currentCol] = null;
                        }
                    }
                }
                //                print_r($returnValue);
                //            echo '<br />';
            }
            return $returnValue;
        }

        private function _parseFormula($formula, PHPExcel_Cell $pCell = null) {
            if (($formula = $this->convertMatrixReferences(trim($formula))) === false) {
                return false;
            }
            //    If we're using cell caching, then $pCell may well be flushed back to the cache (which detaches the parent worksheet),
            //        so we store the parent worksheet so that we can re-attach it when necessary
            $pCellParent = ($pCell !== null) ? $pCell->getWorksheet() : null;
            $regexpMatchString = '/^(' . self::CALCULATION_REGEXP_FUNCTION . '|' . self::CALCULATION_REGEXP_CELLREF . '|' . self::CALCULATION_REGEXP_NUMBER . '|' . self::CALCULATION_REGEXP_STRING . '|' . self::CALCULATION_REGEXP_OPENBRACE . '|' . self::CALCULATION_REGEXP_NAMEDRANGE . '|' . self::CALCULATION_REGEXP_ERROR . ')/si';
            //    Start with initialisation
            $index             = 0;
            $stack             = new PHPExcel_Calculation_Token_Stack;
            $output            = [];
            $expectingOperator = false;                    //    We use this test in syntax-checking the expression to determine when a
            //        - is a negation or + is a positive operator rather than an operation
            $expectingOperand = false;                    //    We use this test in syntax-checking the expression to determine whether an operand
            //        should be null in a function call
            //    The guts of the lexical parser
            //    Loop through the formula extracting each operator and operand in turn
            while (true) {
                //echo 'Assessing Expression '.substr($formula, $index), PHP_EOL;
                $opCharacter = $formula{$index};    //    Get the first character of the value at the current index position
                //echo 'Initial character of expression block is '.$opCharacter, PHP_EOL;
                if ((isset(self::$comparisonOperators[$opCharacter])) && (strlen($formula) > $index) && (isset(self::$comparisonOperators[$formula{$index + 1}]))) {
                    $opCharacter .= $formula{++$index};
                    //echo 'Initial character of expression block is comparison operator '.$opCharacter.PHP_EOL;
                }
                //    Find out if we're currently at the beginning of a number, variable, cell reference, function, parenthesis or operand
                $isOperandOrFunction = preg_match($regexpMatchString, substr($formula, $index), $match);
                //echo '$isOperandOrFunction is '.(($isOperandOrFunction) ? 'True' : 'False').PHP_EOL;
                //var_dump($match);
                if ($opCharacter == '-' && !$expectingOperator) {                //    Is it a negation instead of a minus?
                    //echo 'Element is a Negation operator', PHP_EOL;
                    $stack->push('Unary Operator', '~');                            //    Put a negation on the stack
                    ++$index;                                                    //        and drop the negation symbol
                } elseif ($opCharacter == '%' && $expectingOperator) {
                    //echo 'Element is a Percentage operator', PHP_EOL;
                    $stack->push('Unary Operator', '%');                            //    Put a percentage on the stack
                    ++$index;
                } elseif ($opCharacter == '+' && !$expectingOperator) {            //    Positive (unary plus rather than binary operator plus) can be discarded?
                    //echo 'Element is a Positive number, not Plus operator', PHP_EOL;
                    ++$index;                                                    //    Drop the redundant plus symbol
                } elseif ((($opCharacter == '~') || ($opCharacter == '|')) && (!$isOperandOrFunction)) {    //    We have to explicitly deny a tilde or pipe, because they are legal
                    return $this->raiseFormulaError("Formula Error: Illegal character '~'");                //        on the stack but not in the input expression
                } elseif ((isset(self::$operators[$opCharacter]) or $isOperandOrFunction) && $expectingOperator) {    //    Are we putting an operator on the stack?
                    //echo 'Element with value '.$opCharacter.' is an Operator', PHP_EOL;
                    while ($stack->count() > 0 && ($o2 = $stack->last()) && isset(self::$operators[$o2['value']]) && @(self::$operatorAssociativity[$opCharacter] ? self::$operatorPrecedence[$opCharacter] < self::$operatorPrecedence[$o2['value']] : self::$operatorPrecedence[$opCharacter] <= self::$operatorPrecedence[$o2['value']])) {
                        $output[] = $stack->pop();                                //    Swap operands and higher precedence operators from the stack to the output
                    }
                    $stack->push('Binary Operator', $opCharacter);    //    Finally put our current operator onto the stack
                    ++$index;
                    $expectingOperator = false;
                } elseif ($opCharacter == ')' && $expectingOperator) {            //    Are we expecting to close a parenthesis?
                    //echo 'Element is a Closing bracket', PHP_EOL;
                    $expectingOperand = false;
                    while (($o2 = $stack->pop()) && $o2['value'] != '(') {        //    Pop off the stack back to the last (
                        if ($o2 === null) {
                            return $this->raiseFormulaError('Formula Error: Unexpected closing brace ")"');
                        } else {
                            $output[] = $o2;
                        }
                    }
                    $d = $stack->last(2);
                    if (preg_match('/^' . self::CALCULATION_REGEXP_FUNCTION . '$/i', $d['value'], $matches)) {    //    Did this parenthesis just close a function?
                        $functionName = $matches[1];                                        //    Get the function name
                        //echo 'Closed Function is '.$functionName, PHP_EOL;
                        $d             = $stack->pop();
                        $argumentCount = $d['value'];        //    See how many arguments there were (argument count is the next value stored on the stack)
                        //if ($argumentCount == 0) {
                        //    echo 'With no arguments', PHP_EOL;
                        //} elseif ($argumentCount == 1) {
                        //    echo 'With 1 argument', PHP_EOL;
                        //} else {
                        //    echo 'With '.$argumentCount.' arguments', PHP_EOL;
                        //}
                        $output[] = $d;                        //    Dump the argument count on the output
                        $output[] = $stack->pop();            //    Pop the function and push onto the output
                        if (isset(self::$controlFunctions[$functionName])) {
                            //echo 'Built-in function '.$functionName, PHP_EOL;
                            $expectedArgumentCount = self::$controlFunctions[$functionName]['argumentCount'];
                            $functionCall          = self::$controlFunctions[$functionName]['functionCall'];
                        } elseif (isset(self::$PHPExcelFunctions[$functionName])) {
                            //echo 'PHPExcel function '.$functionName, PHP_EOL;
                            $expectedArgumentCount = self::$PHPExcelFunctions[$functionName]['argumentCount'];
                            $functionCall          = self::$PHPExcelFunctions[$functionName]['functionCall'];
                        } else {    // did we somehow push a non-function on the stack? this should never happen
                            return $this->raiseFormulaError("Formula Error: Internal error, non-function on stack");
                        }
                        //    Check the argument count
                        $argumentCountError = false;
                        if (is_numeric($expectedArgumentCount)) {
                            if ($expectedArgumentCount < 0) {
                                //echo '$expectedArgumentCount is between 0 and '.abs($expectedArgumentCount), PHP_EOL;
                                if ($argumentCount > abs($expectedArgumentCount)) {
                                    $argumentCountError          = true;
                                    $expectedArgumentCountString = 'no more than ' . abs($expectedArgumentCount);
                                }
                            } else {
                                //echo '$expectedArgumentCount is numeric '.$expectedArgumentCount, PHP_EOL;
                                if ($argumentCount != $expectedArgumentCount) {
                                    $argumentCountError          = true;
                                    $expectedArgumentCountString = $expectedArgumentCount;
                                }
                            }
                        } elseif ($expectedArgumentCount != '*') {
                            $isOperandOrFunction = preg_match('/(\d*)([-+,])(\d*)/', $expectedArgumentCount, $argMatch);
                            //print_r($argMatch);
                            //echo PHP_EOL;
                            switch ($argMatch[2]) {
                                case '+':
                                    if ($argumentCount < $argMatch[1]) {
                                        $argumentCountError          = true;
                                        $expectedArgumentCountString = $argMatch[1] . ' or more ';
                                    }
                                    break;
                                case '-':
                                    if (($argumentCount < $argMatch[1]) || ($argumentCount > $argMatch[3])) {
                                        $argumentCountError          = true;
                                        $expectedArgumentCountString = 'between ' . $argMatch[1] . ' and ' . $argMatch[3];
                                    }
                                    break;
                                case ',':
                                    if (($argumentCount != $argMatch[1]) && ($argumentCount != $argMatch[3])) {
                                        $argumentCountError          = true;
                                        $expectedArgumentCountString = 'either ' . $argMatch[1] . ' or ' . $argMatch[3];
                                    }
                                    break;
                            }
                        }
                        if ($argumentCountError) {
                            return $this->raiseFormulaError("Formula Error: Wrong number of arguments for $functionName() function: $argumentCount given, " . $expectedArgumentCountString . " expected");
                        }
                    }
                    ++$index;
                } elseif ($opCharacter == ',') {            //    Is this the separator for function arguments?
                    //echo 'Element is a Function argument separator', PHP_EOL;
                    while (($o2 = $stack->pop()) && $o2['value'] != '(') {        //    Pop off the stack back to the last (
                        if ($o2 === null) {
                            return $this->raiseFormulaError("Formula Error: Unexpected ,");
                        } else {
                            $output[] = $o2;    // pop the argument expression stuff and push onto the output
                        }
                    }
                    //    If we've a comma when we're expecting an operand, then what we actually have is a null operand;
                    //        so push a null onto the stack
                    if (($expectingOperand) || (!$expectingOperator)) {
                        $output[] = [
                            'type'      => 'NULL Value',
                            'value'     => self::$excelConstants['NULL'],
                            'reference' => null
                        ];
                    }
                    // make sure there was a function
                    $d = $stack->last(2);
                    if (!preg_match('/^' . self::CALCULATION_REGEXP_FUNCTION . '$/i', $d['value'], $matches)) {
                        return $this->raiseFormulaError("Formula Error: Unexpected ,");
                    }
                    $d = $stack->pop();
                    $stack->push($d['type'], ++$d['value'], $d['reference']);    // increment the argument count
                    $stack->push('Brace', '(');    // put the ( back on, we'll need to pop back to it again
                    $expectingOperator = false;
                    $expectingOperand  = true;
                    ++$index;
                } elseif ($opCharacter == '(' && !$expectingOperator) {
                    //                echo 'Element is an Opening Bracket<br />';
                    $stack->push('Brace', '(');
                    ++$index;
                } elseif ($isOperandOrFunction && !$expectingOperator) {    // do we now have a function/variable/number?
                    $expectingOperator = true;
                    $expectingOperand  = false;
                    $val               = $match[1];
                    $length            = strlen($val);
                    //                echo 'Element with value '.$val.' is an Operand, Variable, Constant, String, Number, Cell Reference or Function<br />';
                    if (preg_match('/^' . self::CALCULATION_REGEXP_FUNCTION . '$/i', $val, $matches)) {
                        $val = preg_replace('/\s/u', '', $val);
                        //                    echo 'Element '.$val.' is a Function<br />';
                        if (isset(self::$PHPExcelFunctions[strtoupper($matches[1])]) || isset(self::$controlFunctions[strtoupper($matches[1])])) {    // it's a function
                            $stack->push('Function', strtoupper($val));
                            $ax = preg_match('/^\s*(\s*\))/ui', substr($formula, $index + $length), $amatch);
                            if ($ax) {
                                $stack->push('Operand Count for Function ' . strtoupper($val) . ')', 0);
                                $expectingOperator = true;
                            } else {
                                $stack->push('Operand Count for Function ' . strtoupper($val) . ')', 1);
                                $expectingOperator = false;
                            }
                            $stack->push('Brace', '(');
                        } else {    // it's a var w/ implicit multiplication
                            $output[] = [
                                'type'      => 'Value',
                                'value'     => $matches[1],
                                'reference' => null
                            ];
                        }
                    } elseif (preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '$/i', $val, $matches)) {
                        //                    echo 'Element '.$val.' is a Cell reference<br />';
                        //    Watch for this case-change when modifying to allow cell references in different worksheets...
                        //    Should only be applied to the actual cell column, not the worksheet name
                        //    If the last entry on the stack was a : operator, then we have a cell range reference
                        $testPrevOp = $stack->last(1);
                        if ($testPrevOp['value'] == ':') {
                            //    If we have a worksheet reference, then we're playing with a 3D reference
                            if ($matches[2] == '') {
                                //    Otherwise, we 'inherit' the worksheet reference from the start cell reference
                                //    The start of the cell range reference should be the last entry in $output
                                $startCellRef = $output[count($output) - 1]['value'];
                                preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '$/i', $startCellRef, $startMatches);
                                if ($startMatches[2] > '') {
                                    $val = $startMatches[2] . '!' . $val;
                                }
                            } else {
                                return $this->raiseFormulaError("3D Range references are not yet supported");
                            }
                        }
                        $output[] = [
                            'type'      => 'Cell Reference',
                            'value'     => $val,
                            'reference' => $val
                        ];
                        //                    $expectingOperator = FALSE;
                    } else {    // it's a variable, constant, string, number or boolean
                        //                    echo 'Element is a Variable, Constant, String, Number or Boolean<br />';
                        //    If the last entry on the stack was a : operator, then we may have a row or column range reference
                        $testPrevOp = $stack->last(1);
                        if ($testPrevOp['value'] == ':') {
                            $startRowColRef = $output[count($output) - 1]['value'];
                            $rangeWS1       = '';
                            if (strpos('!', $startRowColRef) !== false) {
                                list($rangeWS1, $startRowColRef) = explode('!', $startRowColRef);
                            }
                            if ($rangeWS1 != '') {
                                $rangeWS1 .= '!';
                            }
                            $rangeWS2 = $rangeWS1;
                            if (strpos('!', $val) !== false) {
                                list($rangeWS2, $val) = explode('!', $val);
                            }
                            if ($rangeWS2 != '') {
                                $rangeWS2 .= '!';
                            }
                            if ((is_integer($startRowColRef)) && (ctype_digit($val)) && ($startRowColRef <= 1048576) && ($val <= 1048576)) {
                                //    Row range
                                $endRowColRef                        = ($pCellParent !== null) ? $pCellParent->getHighestColumn() : 'XFD';    //    Max 16,384 columns for Excel2007
                                $output[count($output) - 1]['value'] = $rangeWS1 . 'A' . $startRowColRef;
                                $val                                 = $rangeWS2 . $endRowColRef . $val;
                            } elseif ((ctype_alpha($startRowColRef)) && (ctype_alpha($val)) && (strlen($startRowColRef) <= 3) && (strlen($val) <= 3)) {
                                //    Column range
                                $endRowColRef                        = ($pCellParent !== null) ? $pCellParent->getHighestRow() : 1048576;        //    Max 1,048,576 rows for Excel2007
                                $output[count($output) - 1]['value'] = $rangeWS1 . strtoupper($startRowColRef) . '1';
                                $val                                 = $rangeWS2 . $val . $endRowColRef;
                            }
                        }
                        $localeConstant = false;
                        if ($opCharacter == '"') {
                            //                        echo 'Element is a String<br />';
                            //    UnEscape any quotes within the string
                            $val = self::wrapResult(str_replace('""', '"', self::unwrapResult($val)));
                        } elseif (is_numeric($val)) {
                            //                        echo 'Element is a Number<br />';
                            if ((strpos($val, '.') !== false) || (stripos($val, 'e') !== false) || ($val > PHP_INT_MAX) || ($val < -PHP_INT_MAX)) {
                                //                            echo 'Casting '.$val.' to float<br />';
                                $val = (float)$val;
                            } else {
                                //                            echo 'Casting '.$val.' to integer<br />';
                                $val = (integer)$val;
                            }
                        } elseif (isset(self::$excelConstants[trim(strtoupper($val))])) {
                            $excelConstant = trim(strtoupper($val));
                            //                        echo 'Element '.$excelConstant.' is an Excel Constant<br />';
                            $val = self::$excelConstants[$excelConstant];
                        } elseif (($localeConstant = array_search(trim(strtoupper($val)), self::$localeBoolean)) !== false) {
                            //                        echo 'Element '.$localeConstant.' is an Excel Constant<br />';
                            $val = self::$excelConstants[$localeConstant];
                        }
                        $details = [
                            'type'      => 'Value',
                            'value'     => $val,
                            'reference' => null
                        ];
                        if ($localeConstant) {
                            $details['localeValue'] = $localeConstant;
                        }
                        $output[] = $details;
                    }
                    $index += $length;
                } elseif ($opCharacter == '$') {    // absolute row or column range
                    ++$index;
                } elseif ($opCharacter == ')') {    // miscellaneous error checking
                    if ($expectingOperand) {
                        $output[]          = [
                            'type'      => 'NULL Value',
                            'value'     => self::$excelConstants['NULL'],
                            'reference' => null
                        ];
                        $expectingOperand  = false;
                        $expectingOperator = true;
                    } else {
                        return $this->raiseFormulaError("Formula Error: Unexpected ')'");
                    }
                } elseif (isset(self::$operators[$opCharacter]) && !$expectingOperator) {
                    return $this->raiseFormulaError("Formula Error: Unexpected operator '$opCharacter'");
                } else {    // I don't even want to know what you did to get here
                    return $this->raiseFormulaError("Formula Error: An unexpected error occured");
                }
                //    Test for end of formula string
                if ($index == strlen($formula)) {
                    //    Did we end with an operator?.
                    //    Only valid for the % unary operator
                    if ((isset(self::$operators[$opCharacter])) && ($opCharacter != '%')) {
                        return $this->raiseFormulaError("Formula Error: Operator '$opCharacter' has no operands");
                    } else {
                        break;
                    }
                }
                //    Ignore white space
                while (($formula{$index} == "\n") || ($formula{$index} == "\r")) {
                    ++$index;
                }
                if ($formula{$index} == ' ') {
                    while ($formula{$index} == ' ') {
                        ++$index;
                    }
                    //    If we're expecting an operator, but only have a space between the previous and next operands (and both are
                    //        Cell References) then we have an INTERSECTION operator
                    //                echo 'Possible Intersect Operator<br />';
                    if (($expectingOperator) && (preg_match('/^' . self::CALCULATION_REGEXP_CELLREF . '.*/Ui', substr($formula, $index), $match)) && ($output[count($output) - 1]['type'] == 'Cell Reference')) {
                        //                    echo 'Element is an Intersect Operator<br />';
                        while ($stack->count() > 0 && ($o2 = $stack->last()) && isset(self::$operators[$o2['value']]) && @(self::$operatorAssociativity[$opCharacter] ? self::$operatorPrecedence[$opCharacter] < self::$operatorPrecedence[$o2['value']] : self::$operatorPrecedence[$opCharacter] <= self::$operatorPrecedence[$o2['value']])) {
                            $output[] = $stack->pop();                                //    Swap operands and higher precedence operators from the stack to the output
                        }
                        $stack->push('Binary Operator', '|');    //    Put an Intersect Operator on the stack
                        $expectingOperator = false;
                    }
                }
            }
            while (($op = $stack->pop()) !== null) {    // pop everything off the stack and push onto output
                if ((is_array($op) && $op['value'] == '(') || ($op === '(')) {
                    return $this->raiseFormulaError("Formula Error: Expecting ')'");    // if there are any opening braces on the stack, then braces were unbalanced
                }
                $output[] = $op;
            }
            return $output;
        }

        private function convertMatrixReferences($formula) {
            static $matrixReplaceFrom = [
                '{',
                ';',
                '}'
            ];
            static $matrixReplaceTo = [
                'MKMATRIX(MKMATRIX(',
                '),MKMATRIX(',
                '))'
            ];
            //    Convert any Excel matrix references to the MKMATRIX() function
            if (strpos($formula, '{') !== false) {
                //    If there is the possibility of braces within a quoted string, then we don't treat those as matrix indicators
                if (strpos($formula, '"') !== false) {
                    //    So instead we skip replacing in any quoted strings by only replacing in every other array element after we've exploded
                    //        the formula
                    $temp = explode('"', $formula);
                    //    Open and Closed counts used for trapping mismatched braces in the formula
                    $openCount = $closeCount = 0;
                    $i         = false;
                    foreach ($temp as &$value) {
                        //    Only count/replace in alternating array entries
                        if ($i = !$i) {
                            $openCount  += substr_count($value, '{');
                            $closeCount += substr_count($value, '}');
                            $value      = str_replace($matrixReplaceFrom, $matrixReplaceTo, $value);
                        }
                    }
                    unset($value);
                    //    Then rebuild the formula string
                    $formula = implode('"', $temp);
                } else {
                    //    If there's no quoted strings, then we do a simple count/replace
                    $openCount  = substr_count($formula, '{');
                    $closeCount = substr_count($formula, '}');
                    $formula    = str_replace($matrixReplaceFrom, $matrixReplaceTo, $formula);
                }
                //    Trap for mismatched braces and trigger an appropriate error
                if ($openCount < $closeCount) {
                    if ($openCount > 0) {
                        return $this->raiseFormulaError("Formula Error: Mismatched matrix braces '}'");
                    } else {
                        return $this->raiseFormulaError("Formula Error: Unexpected '}' encountered");
                    }
                } elseif ($openCount > $closeCount) {
                    if ($closeCount > 0) {
                        return $this->raiseFormulaError("Formula Error: Mismatched matrix braces '{'");
                    } else {
                        return $this->raiseFormulaError("Formula Error: Unexpected '{' encountered");
                    }
                }
            }
            return $formula;
        }

        public function saveValueToCache($cellReference, $cellValue) {
            if ($this->calculationCacheEnabled) {
                $this->calculationCache[$cellReference] = $cellValue;
            }
        }

        /**
         * Validate and parse a formula string
         * @param    string $formula Formula to parse
         * @return    array
         * @throws    PHPExcel_Calculation_Exception
         */
        public function parseFormula($formula) {
            //    Basic validation that this is indeed a formula
            //    We return an empty array if not
            $formula = trim($formula);
            if ((!isset($formula{0})) || ($formula{0} != '=')) {
                return [];
            }
            $formula = ltrim(substr($formula, 1));
            if (!isset($formula{0})) {
                return [];
            }
            //    Parse the formula and return the token stack
            return $this->_parseFormula($formula);
        }


        // trigger an error, but nicely, if need be

        /**
         * Calculate the value of a formula
         * @param    string        $formula Formula to parse
         * @param    string        $cellID  Address of the cell to calculate
         * @param    PHPExcel_Cell $pCell   Cell to calculate
         * @return    mixed
         * @throws    PHPExcel_Calculation_Exception
         */
        public function calculateFormula($formula, $cellID = null, PHPExcel_Cell $pCell = null) {
            //    Initialise the logging settings
            $this->formulaError = null;
            $this->_debugLog->clearLog();
            $this->cyclicReferenceStack->clear();
            if ($this->workbook !== null && $cellID === null && $pCell === null) {
                $cellID = 'A1';
                $pCell  = $this->workbook->getActiveSheet()->getCell($cellID);
            } else {
                //    Disable calculation cacheing because it only applies to cell calculations, not straight formulae
                //    But don't actually flush any cache
                $resetCache                    = $this->getCalculationCacheEnabled();
                $this->calculationCacheEnabled = false;
            }
            //    Execute the calculation
            try {
                $result = self::unwrapResult($this->_calculateFormulaValue($formula, $cellID, $pCell));
            } catch (PHPExcel_Exception $e) {
                throw new PHPExcel_Calculation_Exception($e->getMessage());
            }
            if ($this->workbook === null) {
                //    Reset calculation cacheing to its previous state
                $this->calculationCacheEnabled = $resetCache;
            }
            return $result;
        }

        /**
         * Is calculation caching enabled?
         * @access    public
         * @return boolean
         */
        public function getCalculationCacheEnabled() {
            return $this->calculationCacheEnabled;
        }

        /**
         * Enable/disable calculation cache
         * @access    public
         * @param boolean $pValue
         */
        public function setCalculationCacheEnabled($pValue = true) {
            $this->calculationCacheEnabled = $pValue;
            $this->clearCalculationCache();
        }

        /**
         * Is a specific function implemented?
         * @param    string $pFunction Function Name
         * @return    boolean
         */
        public function isImplemented($pFunction = '') {
            $pFunction = strtoupper($pFunction);
            if (isset(self::$PHPExcelFunctions[$pFunction])) {
                return (self::$PHPExcelFunctions[$pFunction]['functionCall'] != 'PHPExcel_Calculation_Functions::DUMMY');
            } else {
                return false;
            }
        }

        /**
         * Get a list of all implemented functions as an array of function objects
         * @return    array of PHPExcel_Calculation_Function
         */
        public function listFunctions() {
            $returnValue = [];
            foreach (self::$PHPExcelFunctions as $functionName => $function) {
                if ($function['functionCall'] != 'PHPExcel_Calculation_Functions::DUMMY') {
                    $returnValue[$functionName] = new PHPExcel_Calculation_Function($function['category'], $functionName, $function['functionCall']
                    );
                }
            }
            return $returnValue;
        }

        /**
         * Get a list of all Excel function names
         * @return    array
         */
        public function listAllFunctionNames() {
            return array_keys(self::$PHPExcelFunctions);
        }

        /**
         * Get a list of implemented Excel function names
         * @return    array
         */
        public function listFunctionNames() {
            $returnValue = [];
            foreach (self::$PHPExcelFunctions as $functionName => $function) {
                if ($function['functionCall'] != 'PHPExcel_Calculation_Functions::DUMMY') {
                    $returnValue[] = $functionName;
                }
            }
            return $returnValue;
        }
    }
